28.25/15.91 MAYBE 30.48/16.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 30.48/16.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.48/16.54 30.48/16.54 30.48/16.54 H-Termination with start terms of the given HASKELL could not be shown: 30.48/16.54 30.48/16.54 (0) HASKELL 30.48/16.54 (1) IFR [EQUIVALENT, 0 ms] 30.48/16.54 (2) HASKELL 30.48/16.54 (3) BR [EQUIVALENT, 0 ms] 30.48/16.54 (4) HASKELL 30.48/16.54 (5) COR [EQUIVALENT, 0 ms] 30.48/16.54 (6) HASKELL 30.48/16.54 (7) LetRed [EQUIVALENT, 11 ms] 30.48/16.54 (8) HASKELL 30.48/16.54 (9) NumRed [SOUND, 0 ms] 30.48/16.54 (10) HASKELL 30.48/16.54 (11) Narrow [SOUND, 0 ms] 30.48/16.54 (12) AND 30.48/16.54 (13) QDP 30.48/16.54 (14) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (15) QDP 30.48/16.54 (16) QDPOrderProof [EQUIVALENT, 42 ms] 30.48/16.54 (17) QDP 30.48/16.54 (18) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (19) QDP 30.48/16.54 (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.48/16.54 (21) YES 30.48/16.54 (22) QDP 30.48/16.54 (23) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (24) QDP 30.48/16.54 (25) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (26) QDP 30.48/16.54 (27) UsableRulesProof [EQUIVALENT, 0 ms] 30.48/16.54 (28) QDP 30.48/16.54 (29) QReductionProof [EQUIVALENT, 0 ms] 30.48/16.54 (30) QDP 30.48/16.54 (31) MNOCProof [EQUIVALENT, 0 ms] 30.48/16.54 (32) QDP 30.48/16.54 (33) InductionCalculusProof [EQUIVALENT, 10 ms] 30.48/16.54 (34) QDP 30.48/16.54 (35) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (36) QDP 30.48/16.54 (37) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (38) QDP 30.48/16.54 (39) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (40) QDP 30.48/16.54 (41) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (42) QDP 30.48/16.54 (43) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (44) QDP 30.48/16.54 (45) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (46) QDP 30.48/16.54 (47) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (48) QDP 30.48/16.54 (49) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (50) QDP 30.48/16.54 (51) MNOCProof [EQUIVALENT, 0 ms] 30.48/16.54 (52) QDP 30.48/16.54 (53) InductionCalculusProof [EQUIVALENT, 0 ms] 30.48/16.54 (54) QDP 30.48/16.54 (55) QDP 30.48/16.54 (56) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.48/16.54 (57) YES 30.48/16.54 (58) QDP 30.48/16.54 (59) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (60) QDP 30.48/16.54 (61) QDPOrderProof [EQUIVALENT, 7 ms] 30.48/16.54 (62) QDP 30.48/16.54 (63) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (64) QDP 30.48/16.54 (65) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.48/16.54 (66) YES 30.48/16.54 (67) QDP 30.48/16.54 (68) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (69) QDP 30.48/16.54 (70) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (71) QDP 30.48/16.54 (72) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (73) QDP 30.48/16.54 (74) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (75) QDP 30.48/16.54 (76) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (77) QDP 30.48/16.54 (78) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (79) QDP 30.48/16.54 (80) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (81) QDP 30.48/16.54 (82) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (83) QDP 30.48/16.54 (84) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (85) QDP 30.48/16.54 (86) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (87) QDP 30.48/16.54 (88) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (89) QDP 30.48/16.54 (90) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (91) QDP 30.48/16.54 (92) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (93) QDP 30.48/16.54 (94) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (95) QDP 30.48/16.54 (96) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (97) QDP 30.48/16.54 (98) DependencyGraphProof [EQUIVALENT, 0 ms] 30.48/16.54 (99) AND 30.48/16.54 (100) QDP 30.48/16.54 (101) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.48/16.54 (102) YES 30.48/16.54 (103) QDP 30.48/16.54 (104) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (105) QDP 30.48/16.54 (106) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (107) QDP 30.48/16.54 (108) TransformationProof [EQUIVALENT, 0 ms] 30.48/16.54 (109) QDP 30.48/16.54 (110) QDPSizeChangeProof [EQUIVALENT, 0 ms] 30.48/16.54 (111) YES 30.48/16.54 (112) Narrow [COMPLETE, 0 ms] 30.48/16.54 (113) TRUE 30.48/16.54 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (0) 30.48/16.54 Obligation: 30.48/16.54 mainModule Main 30.48/16.54 module Main where { 30.48/16.54 import qualified Prelude; 30.48/16.54 } 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (1) IFR (EQUIVALENT) 30.48/16.54 If Reductions: 30.48/16.54 The following If expression 30.48/16.54 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 30.48/16.54 is transformed to 30.48/16.54 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 30.48/16.54 primModNatS0 x y False = Succ x; 30.48/16.54 " 30.48/16.54 The following If expression 30.48/16.54 "if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x" 30.48/16.54 is transformed to 30.48/16.54 "primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y); 30.48/16.54 primModNatP0 x y False = primMinusNatS y x; 30.48/16.54 " 30.48/16.54 The following If expression 30.48/16.54 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 30.48/16.54 is transformed to 30.48/16.54 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 30.48/16.54 primDivNatS0 x y False = Zero; 30.48/16.54 " 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (2) 30.48/16.54 Obligation: 30.48/16.54 mainModule Main 30.48/16.54 module Main where { 30.48/16.54 import qualified Prelude; 30.48/16.54 } 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (3) BR (EQUIVALENT) 30.48/16.54 Replaced joker patterns by fresh variables and removed binding patterns. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (4) 30.48/16.54 Obligation: 30.48/16.54 mainModule Main 30.48/16.54 module Main where { 30.48/16.54 import qualified Prelude; 30.48/16.54 } 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (5) COR (EQUIVALENT) 30.48/16.54 Cond Reductions: 30.48/16.54 The following Function with conditions 30.48/16.54 "undefined |Falseundefined; 30.48/16.54 " 30.48/16.54 is transformed to 30.48/16.54 "undefined = undefined1; 30.48/16.54 " 30.48/16.54 "undefined0 True = undefined; 30.48/16.54 " 30.48/16.54 "undefined1 = undefined0 False; 30.48/16.54 " 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (6) 30.48/16.54 Obligation: 30.48/16.54 mainModule Main 30.48/16.54 module Main where { 30.48/16.54 import qualified Prelude; 30.48/16.54 } 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (7) LetRed (EQUIVALENT) 30.48/16.54 Let/Where Reductions: 30.48/16.54 The bindings of the following Let/Where expression 30.48/16.54 "(showChar '[') . (shows x) . showl xs where { 30.48/16.54 showl [] = showChar ']'; 30.48/16.54 showl (x : xs) = (showChar ',') . (shows x) . showl xs; 30.48/16.54 } 30.48/16.54 " 30.48/16.54 are unpacked to the following functions on top level 30.48/16.54 "showListShowl [] = showChar ']'; 30.48/16.54 showListShowl (x : xs) = (showChar ',') . (shows x) . showListShowl xs; 30.48/16.54 " 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (8) 30.48/16.54 Obligation: 30.48/16.54 mainModule Main 30.48/16.54 module Main where { 30.48/16.54 import qualified Prelude; 30.48/16.54 } 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (9) NumRed (SOUND) 30.48/16.54 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (10) 30.48/16.54 Obligation: 30.48/16.54 mainModule Main 30.48/16.54 module Main where { 30.48/16.54 import qualified Prelude; 30.48/16.54 } 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (11) Narrow (SOUND) 30.48/16.54 Haskell To QDPs 30.48/16.54 30.48/16.54 digraph dp_graph { 30.48/16.54 node [outthreshold=100, inthreshold=100];1[label="showList",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 30.48/16.54 3[label="showList ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 30.48/16.54 4[label="showList ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];1310[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 1310[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1310 -> 5[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1311[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1311[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1311 -> 6[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 5[label="showList (ww30 : ww31) ww4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 30.48/16.54 6[label="showList [] ww4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 30.48/16.54 7 -> 9[label="",style="dashed", color="red", weight=0]; 30.48/16.54 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]; 30.48/16.54 7 -> 11[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 7 -> 12[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 7 -> 13[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 8 -> 18[label="",style="dashed", color="red", weight=0]; 30.48/16.54 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]; 30.48/16.54 8 -> 20[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 8 -> 21[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 10[label="ww4",fontsize=16,color="green",shape="box"];11[label="ww31",fontsize=16,color="green",shape="box"];12[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"];13[label="ww30",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]; 30.48/16.54 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 (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];20[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"];21[label="ww4",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]; 30.48/16.54 17 -> 137[label="",style="dashed", color="red", weight=0]; 30.48/16.54 17[label="showChar (Char (Succ ww6)) ((shows ww7) . showListShowl ww8)",fontsize=16,color="magenta"];17 -> 138[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 17 -> 139[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 25 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 25[label="(++) (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="magenta"];25 -> 307[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 25 -> 308[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 138[label="ww6",fontsize=16,color="green",shape="box"];139[label="(shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="box"];139 -> 142[label="",style="solid", color="black", weight=3]; 30.48/16.54 137[label="showChar (Char (Succ ww35)) ww36",fontsize=16,color="black",shape="triangle"];137 -> 143[label="",style="solid", color="black", weight=3]; 30.48/16.54 307[label="ww16",fontsize=16,color="green",shape="box"];308[label="Char (Succ ww14) : Char (Succ ww15) : []",fontsize=16,color="green",shape="box"];306[label="ww73 ++ ww62",fontsize=16,color="burlywood",shape="triangle"];1312[label="ww73/ww730 : ww731",fontsize=10,color="white",style="solid",shape="box"];306 -> 1312[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1312 -> 412[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1313[label="ww73/[]",fontsize=10,color="white",style="solid",shape="box"];306 -> 1313[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1313 -> 413[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 142[label="shows ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];142 -> 144[label="",style="solid", color="black", weight=3]; 30.48/16.54 143[label="(:) Char (Succ ww35) ww36",fontsize=16,color="green",shape="box"];412[label="(ww730 : ww731) ++ ww62",fontsize=16,color="black",shape="box"];412 -> 434[label="",style="solid", color="black", weight=3]; 30.48/16.54 413[label="[] ++ ww62",fontsize=16,color="black",shape="box"];413 -> 435[label="",style="solid", color="black", weight=3]; 30.48/16.54 144[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="blue",shape="box"];1314[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1314[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1314 -> 145[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1315[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1315[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1315 -> 146[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1316[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1316[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1316 -> 147[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1317[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1317[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1317 -> 148[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1318[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1318[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1318 -> 149[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1319[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1319[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1319 -> 150[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1320[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1320[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1320 -> 151[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1321[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1321[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1321 -> 152[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1322[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1322[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1322 -> 153[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1323[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1323[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1323 -> 154[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1324[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1324[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1324 -> 155[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1325[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1325[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1325 -> 156[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1326[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1326[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1326 -> 157[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1327[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1327[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1327 -> 158[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1328[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1328[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1328 -> 159[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1329[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1329[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1329 -> 160[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1330[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1330[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1330 -> 161[label="",style="solid", color="blue", weight=3]; 30.48/16.54 1331[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1331[label="",style="solid", color="blue", weight=9]; 30.48/16.54 1331 -> 162[label="",style="solid", color="blue", weight=3]; 30.48/16.54 434[label="ww730 : ww731 ++ ww62",fontsize=16,color="green",shape="box"];434 -> 440[label="",style="dashed", color="green", weight=3]; 30.48/16.54 435[label="ww62",fontsize=16,color="green",shape="box"];145[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];145 -> 163[label="",style="solid", color="black", weight=3]; 30.48/16.54 146[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];146 -> 164[label="",style="solid", color="black", weight=3]; 30.48/16.54 147[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];147 -> 165[label="",style="solid", color="black", weight=3]; 30.48/16.54 148[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];148 -> 166[label="",style="solid", color="black", weight=3]; 30.48/16.54 149[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];149 -> 167[label="",style="solid", color="black", weight=3]; 30.48/16.54 150[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];150 -> 168[label="",style="solid", color="black", weight=3]; 30.48/16.54 151[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];151 -> 169[label="",style="solid", color="black", weight=3]; 30.48/16.54 152[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];152 -> 170[label="",style="solid", color="black", weight=3]; 30.48/16.54 153[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];153 -> 171[label="",style="solid", color="black", weight=3]; 30.48/16.54 154[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];154 -> 172[label="",style="solid", color="black", weight=3]; 30.48/16.54 155[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];155 -> 173[label="",style="solid", color="black", weight=3]; 30.48/16.54 156[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];156 -> 174[label="",style="solid", color="black", weight=3]; 30.48/16.54 157[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];157 -> 175[label="",style="solid", color="black", weight=3]; 30.48/16.54 158[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];158 -> 176[label="",style="solid", color="black", weight=3]; 30.48/16.54 159[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];159 -> 177[label="",style="solid", color="black", weight=3]; 30.48/16.54 160[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];160 -> 178[label="",style="solid", color="black", weight=3]; 30.48/16.54 161[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];161 -> 179[label="",style="solid", color="black", weight=3]; 30.48/16.54 162[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];162 -> 180[label="",style="solid", color="black", weight=3]; 30.48/16.54 440 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 440[label="ww731 ++ ww62",fontsize=16,color="magenta"];440 -> 449[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 163 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 163[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];163 -> 313[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 163 -> 314[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 164 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 164[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];164 -> 315[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 164 -> 316[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 165 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 165[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];165 -> 317[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 165 -> 318[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 166 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 166[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];166 -> 319[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 166 -> 320[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 167 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 167[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];167 -> 321[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 167 -> 322[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 168 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 168[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];168 -> 323[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 168 -> 324[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 169 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 169[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];169 -> 325[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 169 -> 326[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 170 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 170[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];170 -> 327[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 170 -> 328[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 171 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 171[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];171 -> 329[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 171 -> 330[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 172 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 172[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];172 -> 331[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 172 -> 332[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 173 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 173[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];173 -> 333[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 173 -> 334[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 174 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 174[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];174 -> 335[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 174 -> 336[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 175 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 175[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];175 -> 337[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 175 -> 338[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 176 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 176[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];176 -> 339[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 176 -> 340[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 177 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 177[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];177 -> 341[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 177 -> 342[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 178 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 178[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];178 -> 343[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 178 -> 344[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 179 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 179[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];179 -> 345[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 179 -> 346[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 180 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 180[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];180 -> 347[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 180 -> 348[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 449[label="ww731",fontsize=16,color="green",shape="box"];313[label="showListShowl ww8 ww9",fontsize=16,color="burlywood",shape="triangle"];1332[label="ww8/ww80 : ww81",fontsize=10,color="white",style="solid",shape="box"];313 -> 1332[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1332 -> 414[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1333[label="ww8/[]",fontsize=10,color="white",style="solid",shape="box"];313 -> 1333[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1333 -> 415[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 314[label="show ww7",fontsize=16,color="black",shape="box"];314 -> 416[label="",style="solid", color="black", weight=3]; 30.48/16.54 315 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 315[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];316[label="show ww7",fontsize=16,color="black",shape="box"];316 -> 417[label="",style="solid", color="black", weight=3]; 30.48/16.54 317 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 317[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];318[label="show ww7",fontsize=16,color="black",shape="box"];318 -> 418[label="",style="solid", color="black", weight=3]; 30.48/16.54 319 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 319[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];320[label="show ww7",fontsize=16,color="black",shape="box"];320 -> 419[label="",style="solid", color="black", weight=3]; 30.48/16.54 321 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 321[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];322[label="show ww7",fontsize=16,color="black",shape="box"];322 -> 420[label="",style="solid", color="black", weight=3]; 30.48/16.54 323 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 323[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];324[label="show ww7",fontsize=16,color="black",shape="box"];324 -> 421[label="",style="solid", color="black", weight=3]; 30.48/16.54 325 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 325[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];326[label="show ww7",fontsize=16,color="black",shape="box"];326 -> 422[label="",style="solid", color="black", weight=3]; 30.48/16.54 327 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 327[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];328[label="show ww7",fontsize=16,color="black",shape="box"];328 -> 423[label="",style="solid", color="black", weight=3]; 30.48/16.54 329 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 329[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];330[label="show ww7",fontsize=16,color="black",shape="box"];330 -> 424[label="",style="solid", color="black", weight=3]; 30.48/16.54 331 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 331[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];332[label="show ww7",fontsize=16,color="black",shape="box"];332 -> 425[label="",style="solid", color="black", weight=3]; 30.48/16.54 333 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 333[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];334[label="show ww7",fontsize=16,color="black",shape="box"];334 -> 426[label="",style="solid", color="black", weight=3]; 30.48/16.54 335 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 335[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];336[label="show ww7",fontsize=16,color="black",shape="box"];336 -> 427[label="",style="solid", color="black", weight=3]; 30.48/16.54 337 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 337[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];338[label="show ww7",fontsize=16,color="black",shape="box"];338 -> 428[label="",style="solid", color="black", weight=3]; 30.48/16.54 339 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 339[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];340[label="show ww7",fontsize=16,color="black",shape="box"];340 -> 429[label="",style="solid", color="black", weight=3]; 30.48/16.54 341 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 341[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];342[label="show ww7",fontsize=16,color="black",shape="box"];342 -> 430[label="",style="solid", color="black", weight=3]; 30.48/16.54 343 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 343[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];344[label="show ww7",fontsize=16,color="black",shape="box"];344 -> 431[label="",style="solid", color="black", weight=3]; 30.48/16.54 345 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 345[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];346[label="show ww7",fontsize=16,color="black",shape="box"];346 -> 432[label="",style="solid", color="black", weight=3]; 30.48/16.54 347 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.54 347[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];348[label="show ww7",fontsize=16,color="black",shape="box"];348 -> 433[label="",style="solid", color="black", weight=3]; 30.48/16.54 414[label="showListShowl (ww80 : ww81) ww9",fontsize=16,color="black",shape="box"];414 -> 436[label="",style="solid", color="black", weight=3]; 30.48/16.54 415[label="showListShowl [] ww9",fontsize=16,color="black",shape="box"];415 -> 437[label="",style="solid", color="black", weight=3]; 30.48/16.54 416[label="error []",fontsize=16,color="red",shape="box"];417[label="error []",fontsize=16,color="red",shape="box"];418[label="error []",fontsize=16,color="red",shape="box"];419[label="error []",fontsize=16,color="red",shape="box"];420[label="error []",fontsize=16,color="red",shape="box"];421[label="primShowInt ww7",fontsize=16,color="burlywood",shape="triangle"];1334[label="ww7/Pos ww70",fontsize=10,color="white",style="solid",shape="box"];421 -> 1334[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1334 -> 438[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1335[label="ww7/Neg ww70",fontsize=10,color="white",style="solid",shape="box"];421 -> 1335[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1335 -> 439[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 422[label="error []",fontsize=16,color="red",shape="box"];423[label="error []",fontsize=16,color="red",shape="box"];424[label="error []",fontsize=16,color="red",shape="box"];425[label="error []",fontsize=16,color="red",shape="box"];426[label="error []",fontsize=16,color="red",shape="box"];427[label="error []",fontsize=16,color="red",shape="box"];428[label="error []",fontsize=16,color="red",shape="box"];429[label="error []",fontsize=16,color="red",shape="box"];430[label="error []",fontsize=16,color="red",shape="box"];431[label="error []",fontsize=16,color="red",shape="box"];432[label="error []",fontsize=16,color="red",shape="box"];433[label="error []",fontsize=16,color="red",shape="box"];436 -> 9[label="",style="dashed", color="red", weight=0]; 30.48/16.54 436[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"];436 -> 441[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 436 -> 442[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 436 -> 443[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 437 -> 137[label="",style="dashed", color="red", weight=0]; 30.48/16.54 437[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"];437 -> 444[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 437 -> 445[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 438[label="primShowInt (Pos ww70)",fontsize=16,color="burlywood",shape="box"];1336[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];438 -> 1336[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1336 -> 446[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1337[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];438 -> 1337[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1337 -> 447[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 439[label="primShowInt (Neg ww70)",fontsize=16,color="black",shape="box"];439 -> 448[label="",style="solid", color="black", weight=3]; 30.48/16.54 441[label="ww81",fontsize=16,color="green",shape="box"];442[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"];443[label="ww80",fontsize=16,color="green",shape="box"];444[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"];445[label="ww9",fontsize=16,color="green",shape="box"];446[label="primShowInt (Pos (Succ ww700))",fontsize=16,color="black",shape="box"];446 -> 450[label="",style="solid", color="black", weight=3]; 30.48/16.54 447[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];447 -> 451[label="",style="solid", color="black", weight=3]; 30.48/16.54 448[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"];448 -> 452[label="",style="dashed", color="green", weight=3]; 30.48/16.54 450 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.54 450[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"];450 -> 453[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 450 -> 454[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 451[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"];452 -> 421[label="",style="dashed", color="red", weight=0]; 30.48/16.54 452[label="primShowInt (Pos ww70)",fontsize=16,color="magenta"];452 -> 455[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 453[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];453 -> 456[label="",style="dashed", color="green", weight=3]; 30.48/16.54 454 -> 421[label="",style="dashed", color="red", weight=0]; 30.48/16.54 454[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];454 -> 457[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 455[label="Pos ww70",fontsize=16,color="green",shape="box"];456[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];456 -> 474[label="",style="solid", color="black", weight=3]; 30.48/16.54 457 -> 461[label="",style="dashed", color="red", weight=0]; 30.48/16.54 457[label="div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];457 -> 462[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 457 -> 463[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 474 -> 485[label="",style="dashed", color="red", weight=0]; 30.48/16.54 474[label="primIntToChar (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];474 -> 486[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 474 -> 487[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 462[label="ww700",fontsize=16,color="green",shape="box"];463[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];461[label="div Pos (Succ ww78) Pos (Succ ww79)",fontsize=16,color="black",shape="triangle"];461 -> 473[label="",style="solid", color="black", weight=3]; 30.48/16.54 486[label="ww700",fontsize=16,color="green",shape="box"];487[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];485[label="primIntToChar (mod Pos (Succ ww81) Pos (Succ ww82))",fontsize=16,color="black",shape="triangle"];485 -> 488[label="",style="solid", color="black", weight=3]; 30.48/16.54 473[label="primDivInt (Pos (Succ ww78)) (Pos (Succ ww79))",fontsize=16,color="black",shape="box"];473 -> 484[label="",style="solid", color="black", weight=3]; 30.48/16.54 488[label="primIntToChar (primModInt (Pos (Succ ww81)) (Pos (Succ ww82)))",fontsize=16,color="black",shape="box"];488 -> 490[label="",style="solid", color="black", weight=3]; 30.48/16.54 484[label="Pos (primDivNatS (Succ ww78) (Succ ww79))",fontsize=16,color="green",shape="box"];484 -> 489[label="",style="dashed", color="green", weight=3]; 30.48/16.54 490[label="primIntToChar (Pos (primModNatS (Succ ww81) (Succ ww82)))",fontsize=16,color="black",shape="box"];490 -> 492[label="",style="solid", color="black", weight=3]; 30.48/16.54 489[label="primDivNatS (Succ ww78) (Succ ww79)",fontsize=16,color="black",shape="triangle"];489 -> 491[label="",style="solid", color="black", weight=3]; 30.48/16.54 492[label="Char (primModNatS (Succ ww81) (Succ ww82))",fontsize=16,color="green",shape="box"];492 -> 495[label="",style="dashed", color="green", weight=3]; 30.48/16.54 491[label="primDivNatS0 ww78 ww79 (primGEqNatS ww78 ww79)",fontsize=16,color="burlywood",shape="box"];1338[label="ww78/Succ ww780",fontsize=10,color="white",style="solid",shape="box"];491 -> 1338[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1338 -> 493[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1339[label="ww78/Zero",fontsize=10,color="white",style="solid",shape="box"];491 -> 1339[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1339 -> 494[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 495[label="primModNatS (Succ ww81) (Succ ww82)",fontsize=16,color="black",shape="triangle"];495 -> 500[label="",style="solid", color="black", weight=3]; 30.48/16.54 493[label="primDivNatS0 (Succ ww780) ww79 (primGEqNatS (Succ ww780) ww79)",fontsize=16,color="burlywood",shape="box"];1340[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];493 -> 1340[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1340 -> 496[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1341[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];493 -> 1341[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1341 -> 497[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 494[label="primDivNatS0 Zero ww79 (primGEqNatS Zero ww79)",fontsize=16,color="burlywood",shape="box"];1342[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];494 -> 1342[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1342 -> 498[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1343[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];494 -> 1343[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1343 -> 499[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 500[label="primModNatS0 ww81 ww82 (primGEqNatS ww81 ww82)",fontsize=16,color="burlywood",shape="box"];1344[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];500 -> 1344[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1344 -> 505[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1345[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];500 -> 1345[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1345 -> 506[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 496[label="primDivNatS0 (Succ ww780) (Succ ww790) (primGEqNatS (Succ ww780) (Succ ww790))",fontsize=16,color="black",shape="box"];496 -> 501[label="",style="solid", color="black", weight=3]; 30.48/16.54 497[label="primDivNatS0 (Succ ww780) Zero (primGEqNatS (Succ ww780) Zero)",fontsize=16,color="black",shape="box"];497 -> 502[label="",style="solid", color="black", weight=3]; 30.48/16.54 498[label="primDivNatS0 Zero (Succ ww790) (primGEqNatS Zero (Succ ww790))",fontsize=16,color="black",shape="box"];498 -> 503[label="",style="solid", color="black", weight=3]; 30.48/16.54 499[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];499 -> 504[label="",style="solid", color="black", weight=3]; 30.48/16.54 505[label="primModNatS0 (Succ ww810) ww82 (primGEqNatS (Succ ww810) ww82)",fontsize=16,color="burlywood",shape="box"];1346[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];505 -> 1346[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1346 -> 512[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1347[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];505 -> 1347[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1347 -> 513[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 506[label="primModNatS0 Zero ww82 (primGEqNatS Zero ww82)",fontsize=16,color="burlywood",shape="box"];1348[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];506 -> 1348[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1348 -> 514[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1349[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];506 -> 1349[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1349 -> 515[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 501 -> 1026[label="",style="dashed", color="red", weight=0]; 30.48/16.54 501[label="primDivNatS0 (Succ ww780) (Succ ww790) (primGEqNatS ww780 ww790)",fontsize=16,color="magenta"];501 -> 1027[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 501 -> 1028[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 501 -> 1029[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 501 -> 1030[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 502[label="primDivNatS0 (Succ ww780) Zero True",fontsize=16,color="black",shape="box"];502 -> 509[label="",style="solid", color="black", weight=3]; 30.48/16.54 503[label="primDivNatS0 Zero (Succ ww790) False",fontsize=16,color="black",shape="box"];503 -> 510[label="",style="solid", color="black", weight=3]; 30.48/16.54 504[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];504 -> 511[label="",style="solid", color="black", weight=3]; 30.48/16.54 512[label="primModNatS0 (Succ ww810) (Succ ww820) (primGEqNatS (Succ ww810) (Succ ww820))",fontsize=16,color="black",shape="box"];512 -> 522[label="",style="solid", color="black", weight=3]; 30.48/16.54 513[label="primModNatS0 (Succ ww810) Zero (primGEqNatS (Succ ww810) Zero)",fontsize=16,color="black",shape="box"];513 -> 523[label="",style="solid", color="black", weight=3]; 30.48/16.54 514[label="primModNatS0 Zero (Succ ww820) (primGEqNatS Zero (Succ ww820))",fontsize=16,color="black",shape="box"];514 -> 524[label="",style="solid", color="black", weight=3]; 30.48/16.54 515[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];515 -> 525[label="",style="solid", color="black", weight=3]; 30.48/16.54 1027[label="ww790",fontsize=16,color="green",shape="box"];1028[label="ww780",fontsize=16,color="green",shape="box"];1029[label="ww790",fontsize=16,color="green",shape="box"];1030[label="ww780",fontsize=16,color="green",shape="box"];1026[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS ww127 ww128)",fontsize=16,color="burlywood",shape="triangle"];1350[label="ww127/Succ ww1270",fontsize=10,color="white",style="solid",shape="box"];1026 -> 1350[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1350 -> 1067[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1351[label="ww127/Zero",fontsize=10,color="white",style="solid",shape="box"];1026 -> 1351[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1351 -> 1068[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 509[label="Succ (primDivNatS (primMinusNatS (Succ ww780) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];509 -> 520[label="",style="dashed", color="green", weight=3]; 30.48/16.54 510[label="Zero",fontsize=16,color="green",shape="box"];511[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];511 -> 521[label="",style="dashed", color="green", weight=3]; 30.48/16.54 522 -> 1087[label="",style="dashed", color="red", weight=0]; 30.48/16.54 522[label="primModNatS0 (Succ ww810) (Succ ww820) (primGEqNatS ww810 ww820)",fontsize=16,color="magenta"];522 -> 1088[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 522 -> 1089[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 522 -> 1090[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 522 -> 1091[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 523[label="primModNatS0 (Succ ww810) Zero True",fontsize=16,color="black",shape="box"];523 -> 534[label="",style="solid", color="black", weight=3]; 30.48/16.54 524[label="primModNatS0 Zero (Succ ww820) False",fontsize=16,color="black",shape="box"];524 -> 535[label="",style="solid", color="black", weight=3]; 30.48/16.54 525[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];525 -> 536[label="",style="solid", color="black", weight=3]; 30.48/16.54 1067[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS (Succ ww1270) ww128)",fontsize=16,color="burlywood",shape="box"];1352[label="ww128/Succ ww1280",fontsize=10,color="white",style="solid",shape="box"];1067 -> 1352[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1352 -> 1079[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1353[label="ww128/Zero",fontsize=10,color="white",style="solid",shape="box"];1067 -> 1353[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1353 -> 1080[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1068[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS Zero ww128)",fontsize=16,color="burlywood",shape="box"];1354[label="ww128/Succ ww1280",fontsize=10,color="white",style="solid",shape="box"];1068 -> 1354[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1354 -> 1081[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1355[label="ww128/Zero",fontsize=10,color="white",style="solid",shape="box"];1068 -> 1355[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1355 -> 1082[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 520 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.54 520[label="primDivNatS (primMinusNatS (Succ ww780) Zero) (Succ Zero)",fontsize=16,color="magenta"];520 -> 1271[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 520 -> 1272[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 520 -> 1273[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 521 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.54 521[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];521 -> 1274[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 521 -> 1275[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 521 -> 1276[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1088[label="ww810",fontsize=16,color="green",shape="box"];1089[label="ww820",fontsize=16,color="green",shape="box"];1090[label="ww820",fontsize=16,color="green",shape="box"];1091[label="ww810",fontsize=16,color="green",shape="box"];1087[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS ww132 ww133)",fontsize=16,color="burlywood",shape="triangle"];1356[label="ww132/Succ ww1320",fontsize=10,color="white",style="solid",shape="box"];1087 -> 1356[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1356 -> 1128[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1357[label="ww132/Zero",fontsize=10,color="white",style="solid",shape="box"];1087 -> 1357[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1357 -> 1129[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 534 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.54 534[label="primModNatS (primMinusNatS (Succ ww810) Zero) (Succ Zero)",fontsize=16,color="magenta"];534 -> 1175[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 534 -> 1176[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 534 -> 1177[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 535[label="Succ Zero",fontsize=16,color="green",shape="box"];536 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.54 536[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];536 -> 1178[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 536 -> 1179[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 536 -> 1180[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1079[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS (Succ ww1270) (Succ ww1280))",fontsize=16,color="black",shape="box"];1079 -> 1130[label="",style="solid", color="black", weight=3]; 30.48/16.54 1080[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS (Succ ww1270) Zero)",fontsize=16,color="black",shape="box"];1080 -> 1131[label="",style="solid", color="black", weight=3]; 30.48/16.54 1081[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS Zero (Succ ww1280))",fontsize=16,color="black",shape="box"];1081 -> 1132[label="",style="solid", color="black", weight=3]; 30.48/16.54 1082[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1082 -> 1133[label="",style="solid", color="black", weight=3]; 30.48/16.54 1271[label="Succ ww780",fontsize=16,color="green",shape="box"];1272[label="Zero",fontsize=16,color="green",shape="box"];1273[label="Zero",fontsize=16,color="green",shape="box"];1270[label="primDivNatS (primMinusNatS ww139 ww140) (Succ ww141)",fontsize=16,color="burlywood",shape="triangle"];1358[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1270 -> 1358[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1358 -> 1295[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1359[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1270 -> 1359[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1359 -> 1296[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1274[label="Zero",fontsize=16,color="green",shape="box"];1275[label="Zero",fontsize=16,color="green",shape="box"];1276[label="Zero",fontsize=16,color="green",shape="box"];1128[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS (Succ ww1320) ww133)",fontsize=16,color="burlywood",shape="box"];1360[label="ww133/Succ ww1330",fontsize=10,color="white",style="solid",shape="box"];1128 -> 1360[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1360 -> 1138[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1361[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1128 -> 1361[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1361 -> 1139[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1129[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS Zero ww133)",fontsize=16,color="burlywood",shape="box"];1362[label="ww133/Succ ww1330",fontsize=10,color="white",style="solid",shape="box"];1129 -> 1362[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1362 -> 1140[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1363[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1129 -> 1363[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1363 -> 1141[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1175[label="Succ ww810",fontsize=16,color="green",shape="box"];1176[label="Zero",fontsize=16,color="green",shape="box"];1177[label="Zero",fontsize=16,color="green",shape="box"];1174[label="primModNatS (primMinusNatS ww135 ww136) (Succ ww137)",fontsize=16,color="burlywood",shape="triangle"];1364[label="ww135/Succ ww1350",fontsize=10,color="white",style="solid",shape="box"];1174 -> 1364[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1364 -> 1205[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1365[label="ww135/Zero",fontsize=10,color="white",style="solid",shape="box"];1174 -> 1365[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1365 -> 1206[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1178[label="Zero",fontsize=16,color="green",shape="box"];1179[label="Zero",fontsize=16,color="green",shape="box"];1180[label="Zero",fontsize=16,color="green",shape="box"];1130 -> 1026[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1130[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS ww1270 ww1280)",fontsize=16,color="magenta"];1130 -> 1142[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1130 -> 1143[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1131[label="primDivNatS0 (Succ ww125) (Succ ww126) True",fontsize=16,color="black",shape="triangle"];1131 -> 1144[label="",style="solid", color="black", weight=3]; 30.48/16.54 1132[label="primDivNatS0 (Succ ww125) (Succ ww126) False",fontsize=16,color="black",shape="box"];1132 -> 1145[label="",style="solid", color="black", weight=3]; 30.48/16.54 1133 -> 1131[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1133[label="primDivNatS0 (Succ ww125) (Succ ww126) True",fontsize=16,color="magenta"];1295[label="primDivNatS (primMinusNatS (Succ ww1390) ww140) (Succ ww141)",fontsize=16,color="burlywood",shape="box"];1366[label="ww140/Succ ww1400",fontsize=10,color="white",style="solid",shape="box"];1295 -> 1366[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1366 -> 1297[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1367[label="ww140/Zero",fontsize=10,color="white",style="solid",shape="box"];1295 -> 1367[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1367 -> 1298[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1296[label="primDivNatS (primMinusNatS Zero ww140) (Succ ww141)",fontsize=16,color="burlywood",shape="box"];1368[label="ww140/Succ ww1400",fontsize=10,color="white",style="solid",shape="box"];1296 -> 1368[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1368 -> 1299[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1369[label="ww140/Zero",fontsize=10,color="white",style="solid",shape="box"];1296 -> 1369[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1369 -> 1300[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1138[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS (Succ ww1320) (Succ ww1330))",fontsize=16,color="black",shape="box"];1138 -> 1152[label="",style="solid", color="black", weight=3]; 30.48/16.54 1139[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS (Succ ww1320) Zero)",fontsize=16,color="black",shape="box"];1139 -> 1153[label="",style="solid", color="black", weight=3]; 30.48/16.54 1140[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS Zero (Succ ww1330))",fontsize=16,color="black",shape="box"];1140 -> 1154[label="",style="solid", color="black", weight=3]; 30.48/16.54 1141[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1141 -> 1155[label="",style="solid", color="black", weight=3]; 30.48/16.54 1205[label="primModNatS (primMinusNatS (Succ ww1350) ww136) (Succ ww137)",fontsize=16,color="burlywood",shape="box"];1370[label="ww136/Succ ww1360",fontsize=10,color="white",style="solid",shape="box"];1205 -> 1370[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1370 -> 1211[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1371[label="ww136/Zero",fontsize=10,color="white",style="solid",shape="box"];1205 -> 1371[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1371 -> 1212[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1206[label="primModNatS (primMinusNatS Zero ww136) (Succ ww137)",fontsize=16,color="burlywood",shape="box"];1372[label="ww136/Succ ww1360",fontsize=10,color="white",style="solid",shape="box"];1206 -> 1372[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1372 -> 1213[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1373[label="ww136/Zero",fontsize=10,color="white",style="solid",shape="box"];1206 -> 1373[label="",style="solid", color="burlywood", weight=9]; 30.48/16.54 1373 -> 1214[label="",style="solid", color="burlywood", weight=3]; 30.48/16.54 1142[label="ww1280",fontsize=16,color="green",shape="box"];1143[label="ww1270",fontsize=16,color="green",shape="box"];1144[label="Succ (primDivNatS (primMinusNatS (Succ ww125) (Succ ww126)) (Succ (Succ ww126)))",fontsize=16,color="green",shape="box"];1144 -> 1156[label="",style="dashed", color="green", weight=3]; 30.48/16.54 1145[label="Zero",fontsize=16,color="green",shape="box"];1297[label="primDivNatS (primMinusNatS (Succ ww1390) (Succ ww1400)) (Succ ww141)",fontsize=16,color="black",shape="box"];1297 -> 1301[label="",style="solid", color="black", weight=3]; 30.48/16.54 1298[label="primDivNatS (primMinusNatS (Succ ww1390) Zero) (Succ ww141)",fontsize=16,color="black",shape="box"];1298 -> 1302[label="",style="solid", color="black", weight=3]; 30.48/16.54 1299[label="primDivNatS (primMinusNatS Zero (Succ ww1400)) (Succ ww141)",fontsize=16,color="black",shape="box"];1299 -> 1303[label="",style="solid", color="black", weight=3]; 30.48/16.54 1300[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww141)",fontsize=16,color="black",shape="box"];1300 -> 1304[label="",style="solid", color="black", weight=3]; 30.48/16.54 1152 -> 1087[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1152[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS ww1320 ww1330)",fontsize=16,color="magenta"];1152 -> 1161[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1152 -> 1162[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1153[label="primModNatS0 (Succ ww130) (Succ ww131) True",fontsize=16,color="black",shape="triangle"];1153 -> 1163[label="",style="solid", color="black", weight=3]; 30.48/16.54 1154[label="primModNatS0 (Succ ww130) (Succ ww131) False",fontsize=16,color="black",shape="box"];1154 -> 1164[label="",style="solid", color="black", weight=3]; 30.48/16.54 1155 -> 1153[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1155[label="primModNatS0 (Succ ww130) (Succ ww131) True",fontsize=16,color="magenta"];1211[label="primModNatS (primMinusNatS (Succ ww1350) (Succ ww1360)) (Succ ww137)",fontsize=16,color="black",shape="box"];1211 -> 1219[label="",style="solid", color="black", weight=3]; 30.48/16.54 1212[label="primModNatS (primMinusNatS (Succ ww1350) Zero) (Succ ww137)",fontsize=16,color="black",shape="box"];1212 -> 1220[label="",style="solid", color="black", weight=3]; 30.48/16.54 1213[label="primModNatS (primMinusNatS Zero (Succ ww1360)) (Succ ww137)",fontsize=16,color="black",shape="box"];1213 -> 1221[label="",style="solid", color="black", weight=3]; 30.48/16.54 1214[label="primModNatS (primMinusNatS Zero Zero) (Succ ww137)",fontsize=16,color="black",shape="box"];1214 -> 1222[label="",style="solid", color="black", weight=3]; 30.48/16.54 1156 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1156[label="primDivNatS (primMinusNatS (Succ ww125) (Succ ww126)) (Succ (Succ ww126))",fontsize=16,color="magenta"];1156 -> 1277[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1156 -> 1278[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1156 -> 1279[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1301 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1301[label="primDivNatS (primMinusNatS ww1390 ww1400) (Succ ww141)",fontsize=16,color="magenta"];1301 -> 1305[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1301 -> 1306[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1302 -> 489[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1302[label="primDivNatS (Succ ww1390) (Succ ww141)",fontsize=16,color="magenta"];1302 -> 1307[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1302 -> 1308[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1303[label="primDivNatS Zero (Succ ww141)",fontsize=16,color="black",shape="triangle"];1303 -> 1309[label="",style="solid", color="black", weight=3]; 30.48/16.54 1304 -> 1303[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1304[label="primDivNatS Zero (Succ ww141)",fontsize=16,color="magenta"];1161[label="ww1330",fontsize=16,color="green",shape="box"];1162[label="ww1320",fontsize=16,color="green",shape="box"];1163 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1163[label="primModNatS (primMinusNatS (Succ ww130) (Succ ww131)) (Succ (Succ ww131))",fontsize=16,color="magenta"];1163 -> 1187[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1163 -> 1188[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1163 -> 1189[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1164[label="Succ (Succ ww130)",fontsize=16,color="green",shape="box"];1219 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1219[label="primModNatS (primMinusNatS ww1350 ww1360) (Succ ww137)",fontsize=16,color="magenta"];1219 -> 1229[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1219 -> 1230[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1220 -> 495[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1220[label="primModNatS (Succ ww1350) (Succ ww137)",fontsize=16,color="magenta"];1220 -> 1231[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1220 -> 1232[label="",style="dashed", color="magenta", weight=3]; 30.48/16.54 1221[label="primModNatS Zero (Succ ww137)",fontsize=16,color="black",shape="triangle"];1221 -> 1233[label="",style="solid", color="black", weight=3]; 30.48/16.54 1222 -> 1221[label="",style="dashed", color="red", weight=0]; 30.48/16.54 1222[label="primModNatS Zero (Succ ww137)",fontsize=16,color="magenta"];1277[label="Succ ww125",fontsize=16,color="green",shape="box"];1278[label="Succ ww126",fontsize=16,color="green",shape="box"];1279[label="Succ ww126",fontsize=16,color="green",shape="box"];1305[label="ww1390",fontsize=16,color="green",shape="box"];1306[label="ww1400",fontsize=16,color="green",shape="box"];1307[label="ww1390",fontsize=16,color="green",shape="box"];1308[label="ww141",fontsize=16,color="green",shape="box"];1309[label="Zero",fontsize=16,color="green",shape="box"];1187[label="Succ ww130",fontsize=16,color="green",shape="box"];1188[label="Succ ww131",fontsize=16,color="green",shape="box"];1189[label="Succ ww131",fontsize=16,color="green",shape="box"];1229[label="ww1350",fontsize=16,color="green",shape="box"];1230[label="ww1360",fontsize=16,color="green",shape="box"];1231[label="ww1350",fontsize=16,color="green",shape="box"];1232[label="ww137",fontsize=16,color="green",shape="box"];1233[label="Zero",fontsize=16,color="green",shape="box"];} 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (12) 30.48/16.54 Complex Obligation (AND) 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (13) 30.48/16.54 Obligation: 30.48/16.54 Q DP problem: 30.48/16.54 The TRS P consists of the following rules: 30.48/16.54 30.48/16.54 new_primDivNatS0(ww125, ww126, Zero, Zero) -> new_primDivNatS00(ww125, ww126) 30.48/16.54 new_primDivNatS00(ww125, ww126) -> new_primDivNatS(Succ(ww125), Succ(ww126), Succ(ww126)) 30.48/16.54 new_primDivNatS(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS(ww1390, ww1400, ww141) 30.48/16.54 new_primDivNatS1(Succ(ww780), Zero) -> new_primDivNatS(Succ(ww780), Zero, Zero) 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS0(ww125, ww126, ww1270, ww1280) 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS(Succ(ww125), Succ(ww126), Succ(ww126)) 30.48/16.54 new_primDivNatS1(Succ(ww780), Succ(ww790)) -> new_primDivNatS0(ww780, ww790, ww780, ww790) 30.48/16.54 new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) 30.48/16.54 new_primDivNatS(Succ(ww1390), Zero, ww141) -> new_primDivNatS1(ww1390, ww141) 30.48/16.54 30.48/16.54 R is empty. 30.48/16.54 Q is empty. 30.48/16.54 We have to consider all minimal (P,Q,R)-chains. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (14) DependencyGraphProof (EQUIVALENT) 30.48/16.54 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (15) 30.48/16.54 Obligation: 30.48/16.54 Q DP problem: 30.48/16.54 The TRS P consists of the following rules: 30.48/16.54 30.48/16.54 new_primDivNatS00(ww125, ww126) -> new_primDivNatS(Succ(ww125), Succ(ww126), Succ(ww126)) 30.48/16.54 new_primDivNatS(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS(ww1390, ww1400, ww141) 30.48/16.54 new_primDivNatS(Succ(ww1390), Zero, ww141) -> new_primDivNatS1(ww1390, ww141) 30.48/16.54 new_primDivNatS1(Succ(ww780), Zero) -> new_primDivNatS(Succ(ww780), Zero, Zero) 30.48/16.54 new_primDivNatS1(Succ(ww780), Succ(ww790)) -> new_primDivNatS0(ww780, ww790, ww780, ww790) 30.48/16.54 new_primDivNatS0(ww125, ww126, Zero, Zero) -> new_primDivNatS00(ww125, ww126) 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS0(ww125, ww126, ww1270, ww1280) 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS(Succ(ww125), Succ(ww126), Succ(ww126)) 30.48/16.54 30.48/16.54 R is empty. 30.48/16.54 Q is empty. 30.48/16.54 We have to consider all minimal (P,Q,R)-chains. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (16) QDPOrderProof (EQUIVALENT) 30.48/16.54 We use the reduction pair processor [LPAR04,JAR06]. 30.48/16.54 30.48/16.54 30.48/16.54 The following pairs can be oriented strictly and are deleted. 30.48/16.54 30.48/16.54 new_primDivNatS(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS(ww1390, ww1400, ww141) 30.48/16.54 new_primDivNatS1(Succ(ww780), Zero) -> new_primDivNatS(Succ(ww780), Zero, Zero) 30.48/16.54 new_primDivNatS1(Succ(ww780), Succ(ww790)) -> new_primDivNatS0(ww780, ww790, ww780, ww790) 30.48/16.54 The remaining pairs can at least be oriented weakly. 30.48/16.54 Used ordering: Polynomial interpretation [POLO]: 30.48/16.54 30.48/16.54 POL(Succ(x_1)) = 1 + x_1 30.48/16.54 POL(Zero) = 0 30.48/16.54 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 30.48/16.54 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 30.48/16.54 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 30.48/16.54 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 30.48/16.54 30.48/16.54 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 30.48/16.54 none 30.48/16.54 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (17) 30.48/16.54 Obligation: 30.48/16.54 Q DP problem: 30.48/16.54 The TRS P consists of the following rules: 30.48/16.54 30.48/16.54 new_primDivNatS00(ww125, ww126) -> new_primDivNatS(Succ(ww125), Succ(ww126), Succ(ww126)) 30.48/16.54 new_primDivNatS(Succ(ww1390), Zero, ww141) -> new_primDivNatS1(ww1390, ww141) 30.48/16.54 new_primDivNatS0(ww125, ww126, Zero, Zero) -> new_primDivNatS00(ww125, ww126) 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS0(ww125, ww126, ww1270, ww1280) 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS(Succ(ww125), Succ(ww126), Succ(ww126)) 30.48/16.54 30.48/16.54 R is empty. 30.48/16.54 Q is empty. 30.48/16.54 We have to consider all minimal (P,Q,R)-chains. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (18) DependencyGraphProof (EQUIVALENT) 30.48/16.54 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (19) 30.48/16.54 Obligation: 30.48/16.54 Q DP problem: 30.48/16.54 The TRS P consists of the following rules: 30.48/16.54 30.48/16.54 new_primDivNatS0(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS0(ww125, ww126, ww1270, ww1280) 30.48/16.54 30.48/16.54 R is empty. 30.48/16.54 Q is empty. 30.48/16.54 We have to consider all minimal (P,Q,R)-chains. 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (20) QDPSizeChangeProof (EQUIVALENT) 30.48/16.54 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. 30.48/16.54 30.48/16.54 From the DPs we obtained the following set of size-change graphs: 30.48/16.54 *new_primDivNatS0(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS0(ww125, ww126, ww1270, ww1280) 30.48/16.54 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 30.48/16.54 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (21) 30.48/16.54 YES 30.48/16.54 30.48/16.54 ---------------------------------------- 30.48/16.54 30.48/16.54 (22) 30.48/16.54 Obligation: 30.48/16.54 Q DP problem: 30.48/16.54 The TRS P consists of the following rules: 30.48/16.54 30.48/16.54 new_primShowInt(Neg(ww70)) -> new_primShowInt(Pos(ww70)) 30.48/16.54 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 30.48/16.54 30.48/16.54 The TRS R consists of the following rules: 30.48/16.54 30.48/16.54 new_div(ww78, ww79) -> Pos(new_primDivNatS3(ww78, ww79)) 30.48/16.54 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.54 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.54 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.54 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.54 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.54 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.54 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.54 new_primDivNatS2(ww141) -> Zero 30.48/16.54 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.54 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_div(x0, x1) 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (23) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (24) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_div(ww78, ww79) -> Pos(new_primDivNatS3(ww78, ww79)) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_div(x0, x1) 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (25) TransformationProof (EQUIVALENT) 30.48/16.55 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]: 30.48/16.55 30.48/16.55 (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))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (26) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_div(ww78, ww79) -> Pos(new_primDivNatS3(ww78, ww79)) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_div(x0, x1) 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (27) UsableRulesProof (EQUIVALENT) 30.48/16.55 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. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (28) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_div(x0, x1) 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (29) QReductionProof (EQUIVALENT) 30.48/16.55 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 30.48/16.55 30.48/16.55 new_div(x0, x1) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (30) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (31) MNOCProof (EQUIVALENT) 30.48/16.55 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (32) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (33) InductionCalculusProof (EQUIVALENT) 30.48/16.55 Note that final constraints are written in bold face. 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 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: 30.48/16.55 *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: 30.48/16.55 30.48/16.55 (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))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 30.48/16.55 30.48/16.55 (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))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 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: 30.48/16.55 30.48/16.55 (3) (new_primDivNatS01(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3) ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 (4) (Succ(new_primDivNatS4(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))))))))))))) 30.48/16.55 30.48/16.55 (5) (Succ(new_primDivNatS4(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))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint: 30.48/16.55 30.48/16.55 (6) (x4=x7 & x3=x8 & new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints: 30.48/16.55 30.48/16.55 (7) (new_primDivNatS02(x10, x9)=Succ(x1) & x10=Zero & x9=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x9 ==> new_primShowInt(Pos(Succ(Succ(x10))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x10), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 (8) (new_primDivNatS02(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 ==> new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 (9) (new_primDivNatS01(x20, x19, x18, x17)=Succ(x1) & x20=Succ(x18) & x19=Succ(x17) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 & (\/x21:new_primDivNatS01(x20, x19, x18, x17)=Succ(x21) & x20=x18 & x19=x17 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We solved constraint (7) using rules (I), (II), (III).We solved constraint (8) using rules (I), (II), (III).We simplified constraint (9) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint: 30.48/16.55 30.48/16.55 (10) (new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 To summarize, we get the following constraints P__>=_ for the following pairs. 30.48/16.55 30.48/16.55 *new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 30.48/16.55 *(new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 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. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (34) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS3(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (35) TransformationProof (EQUIVALENT) 30.48/16.55 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]: 30.48/16.55 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))),new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 30.48/16.55 (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (36) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 30.48/16.55 new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (37) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (38) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (39) TransformationProof (EQUIVALENT) 30.48/16.55 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))) 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))),new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (40) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)) 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (41) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (42) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (43) TransformationProof (EQUIVALENT) 30.48/16.55 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))) 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (44) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)) 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (45) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (46) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (47) TransformationProof (EQUIVALENT) 30.48/16.55 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))) 30.48/16.55 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (48) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)) 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (49) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (50) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (51) MNOCProof (EQUIVALENT) 30.48/16.55 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (52) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (53) InductionCalculusProof (EQUIVALENT) 30.48/16.55 Note that final constraints are written in bold face. 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) the following chains were created: 30.48/16.55 *We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))), new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x1))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x1, Succ(Succ(Succ(Succ(Succ(Zero)))))))) which results in the following constraint: 30.48/16.55 30.48/16.55 (1) (new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))=new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 30.48/16.55 30.48/16.55 (2) (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 30.48/16.55 30.48/16.55 (3) (new_primDivNatS02(x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x6 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x5 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 (4) (new_primDivNatS02(x12, x11)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x10))))=x12 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x10))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 (5) (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x13) & (\/x17:new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x17))))) & Succ(Succ(Succ(x14)))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x13 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x14)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x14))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x14, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We solved constraint (3) using rules (I), (II).We solved constraint (4) using rules (I), (II).We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: 30.48/16.55 30.48/16.55 (6) (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Zero))))=x13 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 30.48/16.55 30.48/16.55 (7) (new_primDivNatS02(x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x19 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x18 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 (8) (new_primDivNatS02(x25, x24)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x23)))))=x25 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x24 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x23)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 (9) (new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x27)))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=Succ(x26) & (\/x30:new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x30))))) & Succ(Succ(Succ(Succ(x27))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=x26 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x27)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x27), Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 We solved constraint (7) using rules (I), (II).We solved constraint (8) using rules (I), (II).We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint: 30.48/16.55 30.48/16.55 (10) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 To summarize, we get the following constraints P__>=_ for the following pairs. 30.48/16.55 30.48/16.55 *new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 30.48/16.55 30.48/16.55 *(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 30.48/16.55 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. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (54) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 30.48/16.55 30.48/16.55 The TRS R consists of the following rules: 30.48/16.55 30.48/16.55 new_primDivNatS3(Succ(ww780), Succ(ww790)) -> new_primDivNatS01(ww780, ww790, ww780, ww790) 30.48/16.55 new_primDivNatS3(Zero, Succ(ww790)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Zero, Succ(ww1280)) -> Zero 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Zero) -> new_primDivNatS02(ww125, ww126) 30.48/16.55 new_primDivNatS01(ww125, ww126, Succ(ww1270), Succ(ww1280)) -> new_primDivNatS01(ww125, ww126, ww1270, ww1280) 30.48/16.55 new_primDivNatS02(ww125, ww126) -> Succ(new_primDivNatS4(Succ(ww125), Succ(ww126), Succ(ww126))) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Succ(ww1400), ww141) -> new_primDivNatS4(ww1390, ww1400, ww141) 30.48/16.55 new_primDivNatS4(Zero, Succ(ww1400), ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Zero, Zero, ww141) -> new_primDivNatS2(ww141) 30.48/16.55 new_primDivNatS4(Succ(ww1390), Zero, ww141) -> new_primDivNatS3(ww1390, ww141) 30.48/16.55 new_primDivNatS3(Succ(ww780), Zero) -> Succ(new_primDivNatS4(Succ(ww780), Zero, Zero)) 30.48/16.55 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS4(Zero, Zero, Zero)) 30.48/16.55 new_primDivNatS2(ww141) -> Zero 30.48/16.55 30.48/16.55 The set Q consists of the following terms: 30.48/16.55 30.48/16.55 new_primDivNatS2(x0) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Zero) 30.48/16.55 new_primDivNatS01(x0, x1, Zero, Succ(x2)) 30.48/16.55 new_primDivNatS4(Zero, Succ(x0), x1) 30.48/16.55 new_primDivNatS3(Succ(x0), Zero) 30.48/16.55 new_primDivNatS3(Zero, Succ(x0)) 30.48/16.55 new_primDivNatS02(x0, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Zero, x1) 30.48/16.55 new_primDivNatS4(Succ(x0), Succ(x1), x2) 30.48/16.55 new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) 30.48/16.55 new_primDivNatS3(Succ(x0), Succ(x1)) 30.48/16.55 new_primDivNatS3(Zero, Zero) 30.48/16.55 new_primDivNatS4(Zero, Zero, x0) 30.48/16.55 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (55) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_psPs(:(ww730, ww731), ww62) -> new_psPs(ww731, ww62) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (56) QDPSizeChangeProof (EQUIVALENT) 30.48/16.55 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. 30.48/16.55 30.48/16.55 From the DPs we obtained the following set of size-change graphs: 30.48/16.55 *new_psPs(:(ww730, ww731), ww62) -> new_psPs(ww731, ww62) 30.48/16.55 The graph contains the following edges 1 > 1, 2 >= 2 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (57) 30.48/16.55 YES 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (58) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primModNatS(Succ(ww1350), Zero, ww137) -> new_primModNatS1(ww1350, ww137) 30.48/16.55 new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) 30.48/16.55 new_primModNatS00(ww130, ww131) -> new_primModNatS(Succ(ww130), Succ(ww131), Succ(ww131)) 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Zero) -> new_primModNatS(Succ(ww130), Succ(ww131), Succ(ww131)) 30.48/16.55 new_primModNatS(Succ(ww1350), Succ(ww1360), ww137) -> new_primModNatS(ww1350, ww1360, ww137) 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Succ(ww1330)) -> new_primModNatS0(ww130, ww131, ww1320, ww1330) 30.48/16.55 new_primModNatS1(Succ(ww810), Succ(ww820)) -> new_primModNatS0(ww810, ww820, ww810, ww820) 30.48/16.55 new_primModNatS0(ww130, ww131, Zero, Zero) -> new_primModNatS00(ww130, ww131) 30.48/16.55 new_primModNatS1(Succ(ww810), Zero) -> new_primModNatS(Succ(ww810), Zero, Zero) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (59) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (60) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primModNatS1(Succ(ww810), Succ(ww820)) -> new_primModNatS0(ww810, ww820, ww810, ww820) 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Zero) -> new_primModNatS(Succ(ww130), Succ(ww131), Succ(ww131)) 30.48/16.55 new_primModNatS(Succ(ww1350), Succ(ww1360), ww137) -> new_primModNatS(ww1350, ww1360, ww137) 30.48/16.55 new_primModNatS(Succ(ww1350), Zero, ww137) -> new_primModNatS1(ww1350, ww137) 30.48/16.55 new_primModNatS1(Succ(ww810), Zero) -> new_primModNatS(Succ(ww810), Zero, Zero) 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Succ(ww1330)) -> new_primModNatS0(ww130, ww131, ww1320, ww1330) 30.48/16.55 new_primModNatS0(ww130, ww131, Zero, Zero) -> new_primModNatS00(ww130, ww131) 30.48/16.55 new_primModNatS00(ww130, ww131) -> new_primModNatS(Succ(ww130), Succ(ww131), Succ(ww131)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (61) QDPOrderProof (EQUIVALENT) 30.48/16.55 We use the reduction pair processor [LPAR04,JAR06]. 30.48/16.55 30.48/16.55 30.48/16.55 The following pairs can be oriented strictly and are deleted. 30.48/16.55 30.48/16.55 new_primModNatS1(Succ(ww810), Succ(ww820)) -> new_primModNatS0(ww810, ww820, ww810, ww820) 30.48/16.55 new_primModNatS(Succ(ww1350), Succ(ww1360), ww137) -> new_primModNatS(ww1350, ww1360, ww137) 30.48/16.55 new_primModNatS1(Succ(ww810), Zero) -> new_primModNatS(Succ(ww810), Zero, Zero) 30.48/16.55 The remaining pairs can at least be oriented weakly. 30.48/16.55 Used ordering: Polynomial interpretation [POLO]: 30.48/16.55 30.48/16.55 POL(Succ(x_1)) = 1 + x_1 30.48/16.55 POL(Zero) = 0 30.48/16.55 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 30.48/16.55 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 30.48/16.55 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 30.48/16.55 POL(new_primModNatS1(x_1, x_2)) = 1 + x_1 30.48/16.55 30.48/16.55 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 30.48/16.55 none 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (62) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Zero) -> new_primModNatS(Succ(ww130), Succ(ww131), Succ(ww131)) 30.48/16.55 new_primModNatS(Succ(ww1350), Zero, ww137) -> new_primModNatS1(ww1350, ww137) 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Succ(ww1330)) -> new_primModNatS0(ww130, ww131, ww1320, ww1330) 30.48/16.55 new_primModNatS0(ww130, ww131, Zero, Zero) -> new_primModNatS00(ww130, ww131) 30.48/16.55 new_primModNatS00(ww130, ww131) -> new_primModNatS(Succ(ww130), Succ(ww131), Succ(ww131)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (63) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (64) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_primModNatS0(ww130, ww131, Succ(ww1320), Succ(ww1330)) -> new_primModNatS0(ww130, ww131, ww1320, ww1330) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (65) QDPSizeChangeProof (EQUIVALENT) 30.48/16.55 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. 30.48/16.55 30.48/16.55 From the DPs we obtained the following set of size-change graphs: 30.48/16.55 *new_primModNatS0(ww130, ww131, Succ(ww1320), Succ(ww1330)) -> new_primModNatS0(ww130, ww131, ww1320, ww1330) 30.48/16.55 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (66) 30.48/16.55 YES 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (67) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_Ratio, ba), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_Maybe, be), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bf), bg), bh), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (68) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(ty_Ratio, ba), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)),new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (69) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_Maybe, be), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bf), bg), bh), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (70) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(ty_Maybe, be), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (71) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bf), bg), bh), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (72) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bf), bg), bh), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (73) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (74) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (75) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (76) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (77) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (78) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(ty_[], cc), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)),new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (79) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (80) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (81) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (82) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (83) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (84) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (85) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (86) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (87) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (88) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (89) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (90) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(app(ty_@2, bb), bc), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (91) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (92) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (93) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (94) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (95) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (96) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, :(ww80, ww81), ww9, ty_HugsException, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, :(x2, x3), z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), x2, x3, z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, :(x2, x3), z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), x2, x3, z2, ty_HugsException, ty_HugsException)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (97) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, :(x2, x3), z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), x2, x3, z2, ty_HugsException, ty_HugsException) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (98) DependencyGraphProof (EQUIVALENT) 30.48/16.55 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (99) 30.48/16.55 Complex Obligation (AND) 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (100) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, :(x2, x3), z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), x2, x3, z2, ty_HugsException, ty_HugsException) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (101) QDPSizeChangeProof (EQUIVALENT) 30.48/16.55 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. 30.48/16.55 30.48/16.55 From the DPs we obtained the following set of size-change graphs: 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, :(x2, x3), z2, 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(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), x2, x3, z2, ty_HugsException, ty_HugsException) 30.48/16.55 The graph contains the following edges 1 >= 1, 3 > 2, 3 > 3, 4 >= 4, 5 >= 5, 6 >= 5, 5 >= 6, 6 >= 6 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (102) 30.48/16.55 YES 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (103) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (104) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(ty_IO, bd), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (105) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (106) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, 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(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)) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (107) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (108) TransformationProof (EQUIVALENT) 30.48/16.55 By instantiating [LPAR04] the rule new_pt(ww6, ww7, ww8, ww9, app(app(ty_Either, ca), cb), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: 30.48/16.55 30.48/16.55 (new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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))) 30.48/16.55 30.48/16.55 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (109) 30.48/16.55 Obligation: 30.48/16.55 Q DP problem: 30.48/16.55 The TRS P consists of the following rules: 30.48/16.55 30.48/16.55 new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) 30.48/16.55 new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 30.48/16.55 R is empty. 30.48/16.55 Q is empty. 30.48/16.55 We have to consider all minimal (P,Q,R)-chains. 30.48/16.55 ---------------------------------------- 30.48/16.55 30.48/16.55 (110) QDPSizeChangeProof (EQUIVALENT) 30.48/16.55 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. 30.48/16.55 30.48/16.55 From the DPs we obtained the following set of size-change graphs: 30.48/16.55 *new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) 30.48/16.55 The graph contains the following edges 1 > 2, 1 > 3, 2 >= 4, 3 >= 5, 3 >= 6 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Ratio, x4), app(ty_Ratio, x4)) -> new_showListShowl(z1, z2, app(ty_Ratio, x4)) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) 30.48/16.55 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.55 30.48/16.55 30.48/16.55 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 *new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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)) 30.48/16.56 The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 30.48/16.56 30.48/16.56 30.48/16.56 ---------------------------------------- 30.48/16.56 30.48/16.56 (111) 30.48/16.56 YES 30.48/16.56 30.48/16.56 ---------------------------------------- 30.48/16.56 30.48/16.56 (112) Narrow (COMPLETE) 30.48/16.56 Haskell To QDPs 30.48/16.56 30.48/16.56 digraph dp_graph { 30.48/16.56 node [outthreshold=100, inthreshold=100];1[label="showList",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 30.48/16.56 3[label="showList ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 30.48/16.56 4[label="showList ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];1310[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 1310[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1310 -> 5[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1311[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1311[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1311 -> 6[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 5[label="showList (ww30 : ww31) ww4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 30.48/16.56 6[label="showList [] ww4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 30.48/16.56 7 -> 9[label="",style="dashed", color="red", weight=0]; 30.48/16.56 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]; 30.48/16.56 7 -> 11[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 7 -> 12[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 7 -> 13[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 8 -> 18[label="",style="dashed", color="red", weight=0]; 30.48/16.56 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]; 30.48/16.56 8 -> 20[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 8 -> 21[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 10[label="ww4",fontsize=16,color="green",shape="box"];11[label="ww31",fontsize=16,color="green",shape="box"];12[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"];13[label="ww30",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]; 30.48/16.56 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 (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];20[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"];21[label="ww4",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]; 30.48/16.56 17 -> 137[label="",style="dashed", color="red", weight=0]; 30.48/16.56 17[label="showChar (Char (Succ ww6)) ((shows ww7) . showListShowl ww8)",fontsize=16,color="magenta"];17 -> 138[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 17 -> 139[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 25 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 25[label="(++) (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="magenta"];25 -> 307[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 25 -> 308[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 138[label="ww6",fontsize=16,color="green",shape="box"];139[label="(shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="box"];139 -> 142[label="",style="solid", color="black", weight=3]; 30.48/16.56 137[label="showChar (Char (Succ ww35)) ww36",fontsize=16,color="black",shape="triangle"];137 -> 143[label="",style="solid", color="black", weight=3]; 30.48/16.56 307[label="ww16",fontsize=16,color="green",shape="box"];308[label="Char (Succ ww14) : Char (Succ ww15) : []",fontsize=16,color="green",shape="box"];306[label="ww73 ++ ww62",fontsize=16,color="burlywood",shape="triangle"];1312[label="ww73/ww730 : ww731",fontsize=10,color="white",style="solid",shape="box"];306 -> 1312[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1312 -> 412[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1313[label="ww73/[]",fontsize=10,color="white",style="solid",shape="box"];306 -> 1313[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1313 -> 413[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 142[label="shows ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];142 -> 144[label="",style="solid", color="black", weight=3]; 30.48/16.56 143[label="(:) Char (Succ ww35) ww36",fontsize=16,color="green",shape="box"];412[label="(ww730 : ww731) ++ ww62",fontsize=16,color="black",shape="box"];412 -> 434[label="",style="solid", color="black", weight=3]; 30.48/16.56 413[label="[] ++ ww62",fontsize=16,color="black",shape="box"];413 -> 435[label="",style="solid", color="black", weight=3]; 30.48/16.56 144[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="blue",shape="box"];1314[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1314[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1314 -> 145[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1315[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1315[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1315 -> 146[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1316[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1316[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1316 -> 147[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1317[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1317[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1317 -> 148[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1318[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1318[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1318 -> 149[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1319[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1319[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1319 -> 150[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1320[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1320[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1320 -> 151[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1321[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1321[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1321 -> 152[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1322[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1322[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1322 -> 153[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1323[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1323[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1323 -> 154[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1324[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1324[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1324 -> 155[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1325[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1325[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1325 -> 156[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1326[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1326[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1326 -> 157[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1327[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1327[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1327 -> 158[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1328[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1328[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1328 -> 159[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1329[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1329[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1329 -> 160[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1330[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1330[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1330 -> 161[label="",style="solid", color="blue", weight=3]; 30.48/16.56 1331[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];144 -> 1331[label="",style="solid", color="blue", weight=9]; 30.48/16.56 1331 -> 162[label="",style="solid", color="blue", weight=3]; 30.48/16.56 434[label="ww730 : ww731 ++ ww62",fontsize=16,color="green",shape="box"];434 -> 440[label="",style="dashed", color="green", weight=3]; 30.48/16.56 435[label="ww62",fontsize=16,color="green",shape="box"];145[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];145 -> 163[label="",style="solid", color="black", weight=3]; 30.48/16.56 146[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];146 -> 164[label="",style="solid", color="black", weight=3]; 30.48/16.56 147[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];147 -> 165[label="",style="solid", color="black", weight=3]; 30.48/16.56 148[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];148 -> 166[label="",style="solid", color="black", weight=3]; 30.48/16.56 149[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];149 -> 167[label="",style="solid", color="black", weight=3]; 30.48/16.56 150[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];150 -> 168[label="",style="solid", color="black", weight=3]; 30.48/16.56 151[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];151 -> 169[label="",style="solid", color="black", weight=3]; 30.48/16.56 152[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];152 -> 170[label="",style="solid", color="black", weight=3]; 30.48/16.56 153[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];153 -> 171[label="",style="solid", color="black", weight=3]; 30.48/16.56 154[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];154 -> 172[label="",style="solid", color="black", weight=3]; 30.48/16.56 155[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];155 -> 173[label="",style="solid", color="black", weight=3]; 30.48/16.56 156[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];156 -> 174[label="",style="solid", color="black", weight=3]; 30.48/16.56 157[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];157 -> 175[label="",style="solid", color="black", weight=3]; 30.48/16.56 158[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];158 -> 176[label="",style="solid", color="black", weight=3]; 30.48/16.56 159[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];159 -> 177[label="",style="solid", color="black", weight=3]; 30.48/16.56 160[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];160 -> 178[label="",style="solid", color="black", weight=3]; 30.48/16.56 161[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];161 -> 179[label="",style="solid", color="black", weight=3]; 30.48/16.56 162[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];162 -> 180[label="",style="solid", color="black", weight=3]; 30.48/16.56 440 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 440[label="ww731 ++ ww62",fontsize=16,color="magenta"];440 -> 449[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 163 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 163[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];163 -> 313[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 163 -> 314[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 164 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 164[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];164 -> 315[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 164 -> 316[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 165 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 165[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];165 -> 317[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 165 -> 318[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 166 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 166[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];166 -> 319[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 166 -> 320[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 167 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 167[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];167 -> 321[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 167 -> 322[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 168 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 168[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];168 -> 323[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 168 -> 324[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 169 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 169[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];169 -> 325[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 169 -> 326[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 170 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 170[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];170 -> 327[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 170 -> 328[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 171 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 171[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];171 -> 329[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 171 -> 330[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 172 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 172[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];172 -> 331[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 172 -> 332[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 173 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 173[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];173 -> 333[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 173 -> 334[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 174 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 174[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];174 -> 335[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 174 -> 336[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 175 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 175[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];175 -> 337[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 175 -> 338[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 176 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 176[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];176 -> 339[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 176 -> 340[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 177 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 177[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];177 -> 341[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 177 -> 342[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 178 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 178[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];178 -> 343[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 178 -> 344[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 179 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 179[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];179 -> 345[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 179 -> 346[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 180 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 180[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];180 -> 347[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 180 -> 348[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 449[label="ww731",fontsize=16,color="green",shape="box"];313[label="showListShowl ww8 ww9",fontsize=16,color="burlywood",shape="triangle"];1332[label="ww8/ww80 : ww81",fontsize=10,color="white",style="solid",shape="box"];313 -> 1332[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1332 -> 414[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1333[label="ww8/[]",fontsize=10,color="white",style="solid",shape="box"];313 -> 1333[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1333 -> 415[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 314[label="show ww7",fontsize=16,color="black",shape="box"];314 -> 416[label="",style="solid", color="black", weight=3]; 30.48/16.56 315 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 315[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];316[label="show ww7",fontsize=16,color="black",shape="box"];316 -> 417[label="",style="solid", color="black", weight=3]; 30.48/16.56 317 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 317[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];318[label="show ww7",fontsize=16,color="black",shape="box"];318 -> 418[label="",style="solid", color="black", weight=3]; 30.48/16.56 319 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 319[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];320[label="show ww7",fontsize=16,color="black",shape="box"];320 -> 419[label="",style="solid", color="black", weight=3]; 30.48/16.56 321 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 321[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];322[label="show ww7",fontsize=16,color="black",shape="box"];322 -> 420[label="",style="solid", color="black", weight=3]; 30.48/16.56 323 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 323[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];324[label="show ww7",fontsize=16,color="black",shape="box"];324 -> 421[label="",style="solid", color="black", weight=3]; 30.48/16.56 325 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 325[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];326[label="show ww7",fontsize=16,color="black",shape="box"];326 -> 422[label="",style="solid", color="black", weight=3]; 30.48/16.56 327 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 327[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];328[label="show ww7",fontsize=16,color="black",shape="box"];328 -> 423[label="",style="solid", color="black", weight=3]; 30.48/16.56 329 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 329[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];330[label="show ww7",fontsize=16,color="black",shape="box"];330 -> 424[label="",style="solid", color="black", weight=3]; 30.48/16.56 331 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 331[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];332[label="show ww7",fontsize=16,color="black",shape="box"];332 -> 425[label="",style="solid", color="black", weight=3]; 30.48/16.56 333 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 333[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];334[label="show ww7",fontsize=16,color="black",shape="box"];334 -> 426[label="",style="solid", color="black", weight=3]; 30.48/16.56 335 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 335[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];336[label="show ww7",fontsize=16,color="black",shape="box"];336 -> 427[label="",style="solid", color="black", weight=3]; 30.48/16.56 337 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 337[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];338[label="show ww7",fontsize=16,color="black",shape="box"];338 -> 428[label="",style="solid", color="black", weight=3]; 30.48/16.56 339 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 339[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];340[label="show ww7",fontsize=16,color="black",shape="box"];340 -> 429[label="",style="solid", color="black", weight=3]; 30.48/16.56 341 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 341[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];342[label="show ww7",fontsize=16,color="black",shape="box"];342 -> 430[label="",style="solid", color="black", weight=3]; 30.48/16.56 343 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 343[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];344[label="show ww7",fontsize=16,color="black",shape="box"];344 -> 431[label="",style="solid", color="black", weight=3]; 30.48/16.56 345 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 345[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];346[label="show ww7",fontsize=16,color="black",shape="box"];346 -> 432[label="",style="solid", color="black", weight=3]; 30.48/16.56 347 -> 313[label="",style="dashed", color="red", weight=0]; 30.48/16.56 347[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];348[label="show ww7",fontsize=16,color="black",shape="box"];348 -> 433[label="",style="solid", color="black", weight=3]; 30.48/16.56 414[label="showListShowl (ww80 : ww81) ww9",fontsize=16,color="black",shape="box"];414 -> 436[label="",style="solid", color="black", weight=3]; 30.48/16.56 415[label="showListShowl [] ww9",fontsize=16,color="black",shape="box"];415 -> 437[label="",style="solid", color="black", weight=3]; 30.48/16.56 416[label="error []",fontsize=16,color="red",shape="box"];417[label="error []",fontsize=16,color="red",shape="box"];418[label="error []",fontsize=16,color="red",shape="box"];419[label="error []",fontsize=16,color="red",shape="box"];420[label="error []",fontsize=16,color="red",shape="box"];421[label="primShowInt ww7",fontsize=16,color="burlywood",shape="triangle"];1334[label="ww7/Pos ww70",fontsize=10,color="white",style="solid",shape="box"];421 -> 1334[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1334 -> 438[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1335[label="ww7/Neg ww70",fontsize=10,color="white",style="solid",shape="box"];421 -> 1335[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1335 -> 439[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 422[label="error []",fontsize=16,color="red",shape="box"];423[label="error []",fontsize=16,color="red",shape="box"];424[label="error []",fontsize=16,color="red",shape="box"];425[label="error []",fontsize=16,color="red",shape="box"];426[label="error []",fontsize=16,color="red",shape="box"];427[label="error []",fontsize=16,color="red",shape="box"];428[label="error []",fontsize=16,color="red",shape="box"];429[label="error []",fontsize=16,color="red",shape="box"];430[label="error []",fontsize=16,color="red",shape="box"];431[label="error []",fontsize=16,color="red",shape="box"];432[label="error []",fontsize=16,color="red",shape="box"];433[label="error []",fontsize=16,color="red",shape="box"];436 -> 9[label="",style="dashed", color="red", weight=0]; 30.48/16.56 436[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"];436 -> 441[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 436 -> 442[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 436 -> 443[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 437 -> 137[label="",style="dashed", color="red", weight=0]; 30.48/16.56 437[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"];437 -> 444[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 437 -> 445[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 438[label="primShowInt (Pos ww70)",fontsize=16,color="burlywood",shape="box"];1336[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];438 -> 1336[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1336 -> 446[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1337[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];438 -> 1337[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1337 -> 447[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 439[label="primShowInt (Neg ww70)",fontsize=16,color="black",shape="box"];439 -> 448[label="",style="solid", color="black", weight=3]; 30.48/16.56 441[label="ww81",fontsize=16,color="green",shape="box"];442[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"];443[label="ww80",fontsize=16,color="green",shape="box"];444[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"];445[label="ww9",fontsize=16,color="green",shape="box"];446[label="primShowInt (Pos (Succ ww700))",fontsize=16,color="black",shape="box"];446 -> 450[label="",style="solid", color="black", weight=3]; 30.48/16.56 447[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];447 -> 451[label="",style="solid", color="black", weight=3]; 30.48/16.56 448[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"];448 -> 452[label="",style="dashed", color="green", weight=3]; 30.48/16.56 450 -> 306[label="",style="dashed", color="red", weight=0]; 30.48/16.56 450[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"];450 -> 453[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 450 -> 454[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 451[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"];452 -> 421[label="",style="dashed", color="red", weight=0]; 30.48/16.56 452[label="primShowInt (Pos ww70)",fontsize=16,color="magenta"];452 -> 455[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 453[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];453 -> 456[label="",style="dashed", color="green", weight=3]; 30.48/16.56 454 -> 421[label="",style="dashed", color="red", weight=0]; 30.48/16.56 454[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];454 -> 457[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 455[label="Pos ww70",fontsize=16,color="green",shape="box"];456[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];456 -> 474[label="",style="solid", color="black", weight=3]; 30.48/16.56 457 -> 461[label="",style="dashed", color="red", weight=0]; 30.48/16.56 457[label="div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];457 -> 462[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 457 -> 463[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 474 -> 485[label="",style="dashed", color="red", weight=0]; 30.48/16.56 474[label="primIntToChar (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];474 -> 486[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 474 -> 487[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 462[label="ww700",fontsize=16,color="green",shape="box"];463[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];461[label="div Pos (Succ ww78) Pos (Succ ww79)",fontsize=16,color="black",shape="triangle"];461 -> 473[label="",style="solid", color="black", weight=3]; 30.48/16.56 486[label="ww700",fontsize=16,color="green",shape="box"];487[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];485[label="primIntToChar (mod Pos (Succ ww81) Pos (Succ ww82))",fontsize=16,color="black",shape="triangle"];485 -> 488[label="",style="solid", color="black", weight=3]; 30.48/16.56 473[label="primDivInt (Pos (Succ ww78)) (Pos (Succ ww79))",fontsize=16,color="black",shape="box"];473 -> 484[label="",style="solid", color="black", weight=3]; 30.48/16.56 488[label="primIntToChar (primModInt (Pos (Succ ww81)) (Pos (Succ ww82)))",fontsize=16,color="black",shape="box"];488 -> 490[label="",style="solid", color="black", weight=3]; 30.48/16.56 484[label="Pos (primDivNatS (Succ ww78) (Succ ww79))",fontsize=16,color="green",shape="box"];484 -> 489[label="",style="dashed", color="green", weight=3]; 30.48/16.56 490[label="primIntToChar (Pos (primModNatS (Succ ww81) (Succ ww82)))",fontsize=16,color="black",shape="box"];490 -> 492[label="",style="solid", color="black", weight=3]; 30.48/16.56 489[label="primDivNatS (Succ ww78) (Succ ww79)",fontsize=16,color="black",shape="triangle"];489 -> 491[label="",style="solid", color="black", weight=3]; 30.48/16.56 492[label="Char (primModNatS (Succ ww81) (Succ ww82))",fontsize=16,color="green",shape="box"];492 -> 495[label="",style="dashed", color="green", weight=3]; 30.48/16.56 491[label="primDivNatS0 ww78 ww79 (primGEqNatS ww78 ww79)",fontsize=16,color="burlywood",shape="box"];1338[label="ww78/Succ ww780",fontsize=10,color="white",style="solid",shape="box"];491 -> 1338[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1338 -> 493[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1339[label="ww78/Zero",fontsize=10,color="white",style="solid",shape="box"];491 -> 1339[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1339 -> 494[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 495[label="primModNatS (Succ ww81) (Succ ww82)",fontsize=16,color="black",shape="triangle"];495 -> 500[label="",style="solid", color="black", weight=3]; 30.48/16.56 493[label="primDivNatS0 (Succ ww780) ww79 (primGEqNatS (Succ ww780) ww79)",fontsize=16,color="burlywood",shape="box"];1340[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];493 -> 1340[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1340 -> 496[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1341[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];493 -> 1341[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1341 -> 497[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 494[label="primDivNatS0 Zero ww79 (primGEqNatS Zero ww79)",fontsize=16,color="burlywood",shape="box"];1342[label="ww79/Succ ww790",fontsize=10,color="white",style="solid",shape="box"];494 -> 1342[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1342 -> 498[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1343[label="ww79/Zero",fontsize=10,color="white",style="solid",shape="box"];494 -> 1343[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1343 -> 499[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 500[label="primModNatS0 ww81 ww82 (primGEqNatS ww81 ww82)",fontsize=16,color="burlywood",shape="box"];1344[label="ww81/Succ ww810",fontsize=10,color="white",style="solid",shape="box"];500 -> 1344[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1344 -> 505[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1345[label="ww81/Zero",fontsize=10,color="white",style="solid",shape="box"];500 -> 1345[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1345 -> 506[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 496[label="primDivNatS0 (Succ ww780) (Succ ww790) (primGEqNatS (Succ ww780) (Succ ww790))",fontsize=16,color="black",shape="box"];496 -> 501[label="",style="solid", color="black", weight=3]; 30.48/16.56 497[label="primDivNatS0 (Succ ww780) Zero (primGEqNatS (Succ ww780) Zero)",fontsize=16,color="black",shape="box"];497 -> 502[label="",style="solid", color="black", weight=3]; 30.48/16.56 498[label="primDivNatS0 Zero (Succ ww790) (primGEqNatS Zero (Succ ww790))",fontsize=16,color="black",shape="box"];498 -> 503[label="",style="solid", color="black", weight=3]; 30.48/16.56 499[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];499 -> 504[label="",style="solid", color="black", weight=3]; 30.48/16.56 505[label="primModNatS0 (Succ ww810) ww82 (primGEqNatS (Succ ww810) ww82)",fontsize=16,color="burlywood",shape="box"];1346[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];505 -> 1346[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1346 -> 512[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1347[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];505 -> 1347[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1347 -> 513[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 506[label="primModNatS0 Zero ww82 (primGEqNatS Zero ww82)",fontsize=16,color="burlywood",shape="box"];1348[label="ww82/Succ ww820",fontsize=10,color="white",style="solid",shape="box"];506 -> 1348[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1348 -> 514[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1349[label="ww82/Zero",fontsize=10,color="white",style="solid",shape="box"];506 -> 1349[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1349 -> 515[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 501 -> 1026[label="",style="dashed", color="red", weight=0]; 30.48/16.56 501[label="primDivNatS0 (Succ ww780) (Succ ww790) (primGEqNatS ww780 ww790)",fontsize=16,color="magenta"];501 -> 1027[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 501 -> 1028[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 501 -> 1029[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 501 -> 1030[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 502[label="primDivNatS0 (Succ ww780) Zero True",fontsize=16,color="black",shape="box"];502 -> 509[label="",style="solid", color="black", weight=3]; 30.48/16.56 503[label="primDivNatS0 Zero (Succ ww790) False",fontsize=16,color="black",shape="box"];503 -> 510[label="",style="solid", color="black", weight=3]; 30.48/16.56 504[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];504 -> 511[label="",style="solid", color="black", weight=3]; 30.48/16.56 512[label="primModNatS0 (Succ ww810) (Succ ww820) (primGEqNatS (Succ ww810) (Succ ww820))",fontsize=16,color="black",shape="box"];512 -> 522[label="",style="solid", color="black", weight=3]; 30.48/16.56 513[label="primModNatS0 (Succ ww810) Zero (primGEqNatS (Succ ww810) Zero)",fontsize=16,color="black",shape="box"];513 -> 523[label="",style="solid", color="black", weight=3]; 30.48/16.56 514[label="primModNatS0 Zero (Succ ww820) (primGEqNatS Zero (Succ ww820))",fontsize=16,color="black",shape="box"];514 -> 524[label="",style="solid", color="black", weight=3]; 30.48/16.56 515[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];515 -> 525[label="",style="solid", color="black", weight=3]; 30.48/16.56 1027[label="ww790",fontsize=16,color="green",shape="box"];1028[label="ww780",fontsize=16,color="green",shape="box"];1029[label="ww790",fontsize=16,color="green",shape="box"];1030[label="ww780",fontsize=16,color="green",shape="box"];1026[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS ww127 ww128)",fontsize=16,color="burlywood",shape="triangle"];1350[label="ww127/Succ ww1270",fontsize=10,color="white",style="solid",shape="box"];1026 -> 1350[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1350 -> 1067[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1351[label="ww127/Zero",fontsize=10,color="white",style="solid",shape="box"];1026 -> 1351[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1351 -> 1068[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 509[label="Succ (primDivNatS (primMinusNatS (Succ ww780) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];509 -> 520[label="",style="dashed", color="green", weight=3]; 30.48/16.56 510[label="Zero",fontsize=16,color="green",shape="box"];511[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];511 -> 521[label="",style="dashed", color="green", weight=3]; 30.48/16.56 522 -> 1087[label="",style="dashed", color="red", weight=0]; 30.48/16.56 522[label="primModNatS0 (Succ ww810) (Succ ww820) (primGEqNatS ww810 ww820)",fontsize=16,color="magenta"];522 -> 1088[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 522 -> 1089[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 522 -> 1090[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 522 -> 1091[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 523[label="primModNatS0 (Succ ww810) Zero True",fontsize=16,color="black",shape="box"];523 -> 534[label="",style="solid", color="black", weight=3]; 30.48/16.56 524[label="primModNatS0 Zero (Succ ww820) False",fontsize=16,color="black",shape="box"];524 -> 535[label="",style="solid", color="black", weight=3]; 30.48/16.56 525[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];525 -> 536[label="",style="solid", color="black", weight=3]; 30.48/16.56 1067[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS (Succ ww1270) ww128)",fontsize=16,color="burlywood",shape="box"];1352[label="ww128/Succ ww1280",fontsize=10,color="white",style="solid",shape="box"];1067 -> 1352[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1352 -> 1079[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1353[label="ww128/Zero",fontsize=10,color="white",style="solid",shape="box"];1067 -> 1353[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1353 -> 1080[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1068[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS Zero ww128)",fontsize=16,color="burlywood",shape="box"];1354[label="ww128/Succ ww1280",fontsize=10,color="white",style="solid",shape="box"];1068 -> 1354[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1354 -> 1081[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1355[label="ww128/Zero",fontsize=10,color="white",style="solid",shape="box"];1068 -> 1355[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1355 -> 1082[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 520 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.56 520[label="primDivNatS (primMinusNatS (Succ ww780) Zero) (Succ Zero)",fontsize=16,color="magenta"];520 -> 1271[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 520 -> 1272[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 520 -> 1273[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 521 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.56 521[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];521 -> 1274[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 521 -> 1275[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 521 -> 1276[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1088[label="ww810",fontsize=16,color="green",shape="box"];1089[label="ww820",fontsize=16,color="green",shape="box"];1090[label="ww820",fontsize=16,color="green",shape="box"];1091[label="ww810",fontsize=16,color="green",shape="box"];1087[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS ww132 ww133)",fontsize=16,color="burlywood",shape="triangle"];1356[label="ww132/Succ ww1320",fontsize=10,color="white",style="solid",shape="box"];1087 -> 1356[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1356 -> 1128[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1357[label="ww132/Zero",fontsize=10,color="white",style="solid",shape="box"];1087 -> 1357[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1357 -> 1129[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 534 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.56 534[label="primModNatS (primMinusNatS (Succ ww810) Zero) (Succ Zero)",fontsize=16,color="magenta"];534 -> 1175[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 534 -> 1176[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 534 -> 1177[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 535[label="Succ Zero",fontsize=16,color="green",shape="box"];536 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.56 536[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];536 -> 1178[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 536 -> 1179[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 536 -> 1180[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1079[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS (Succ ww1270) (Succ ww1280))",fontsize=16,color="black",shape="box"];1079 -> 1130[label="",style="solid", color="black", weight=3]; 30.48/16.56 1080[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS (Succ ww1270) Zero)",fontsize=16,color="black",shape="box"];1080 -> 1131[label="",style="solid", color="black", weight=3]; 30.48/16.56 1081[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS Zero (Succ ww1280))",fontsize=16,color="black",shape="box"];1081 -> 1132[label="",style="solid", color="black", weight=3]; 30.48/16.56 1082[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1082 -> 1133[label="",style="solid", color="black", weight=3]; 30.48/16.56 1271[label="Succ ww780",fontsize=16,color="green",shape="box"];1272[label="Zero",fontsize=16,color="green",shape="box"];1273[label="Zero",fontsize=16,color="green",shape="box"];1270[label="primDivNatS (primMinusNatS ww139 ww140) (Succ ww141)",fontsize=16,color="burlywood",shape="triangle"];1358[label="ww139/Succ ww1390",fontsize=10,color="white",style="solid",shape="box"];1270 -> 1358[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1358 -> 1295[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1359[label="ww139/Zero",fontsize=10,color="white",style="solid",shape="box"];1270 -> 1359[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1359 -> 1296[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1274[label="Zero",fontsize=16,color="green",shape="box"];1275[label="Zero",fontsize=16,color="green",shape="box"];1276[label="Zero",fontsize=16,color="green",shape="box"];1128[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS (Succ ww1320) ww133)",fontsize=16,color="burlywood",shape="box"];1360[label="ww133/Succ ww1330",fontsize=10,color="white",style="solid",shape="box"];1128 -> 1360[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1360 -> 1138[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1361[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1128 -> 1361[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1361 -> 1139[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1129[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS Zero ww133)",fontsize=16,color="burlywood",shape="box"];1362[label="ww133/Succ ww1330",fontsize=10,color="white",style="solid",shape="box"];1129 -> 1362[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1362 -> 1140[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1363[label="ww133/Zero",fontsize=10,color="white",style="solid",shape="box"];1129 -> 1363[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1363 -> 1141[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1175[label="Succ ww810",fontsize=16,color="green",shape="box"];1176[label="Zero",fontsize=16,color="green",shape="box"];1177[label="Zero",fontsize=16,color="green",shape="box"];1174[label="primModNatS (primMinusNatS ww135 ww136) (Succ ww137)",fontsize=16,color="burlywood",shape="triangle"];1364[label="ww135/Succ ww1350",fontsize=10,color="white",style="solid",shape="box"];1174 -> 1364[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1364 -> 1205[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1365[label="ww135/Zero",fontsize=10,color="white",style="solid",shape="box"];1174 -> 1365[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1365 -> 1206[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1178[label="Zero",fontsize=16,color="green",shape="box"];1179[label="Zero",fontsize=16,color="green",shape="box"];1180[label="Zero",fontsize=16,color="green",shape="box"];1130 -> 1026[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1130[label="primDivNatS0 (Succ ww125) (Succ ww126) (primGEqNatS ww1270 ww1280)",fontsize=16,color="magenta"];1130 -> 1142[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1130 -> 1143[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1131[label="primDivNatS0 (Succ ww125) (Succ ww126) True",fontsize=16,color="black",shape="triangle"];1131 -> 1144[label="",style="solid", color="black", weight=3]; 30.48/16.56 1132[label="primDivNatS0 (Succ ww125) (Succ ww126) False",fontsize=16,color="black",shape="box"];1132 -> 1145[label="",style="solid", color="black", weight=3]; 30.48/16.56 1133 -> 1131[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1133[label="primDivNatS0 (Succ ww125) (Succ ww126) True",fontsize=16,color="magenta"];1295[label="primDivNatS (primMinusNatS (Succ ww1390) ww140) (Succ ww141)",fontsize=16,color="burlywood",shape="box"];1366[label="ww140/Succ ww1400",fontsize=10,color="white",style="solid",shape="box"];1295 -> 1366[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1366 -> 1297[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1367[label="ww140/Zero",fontsize=10,color="white",style="solid",shape="box"];1295 -> 1367[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1367 -> 1298[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1296[label="primDivNatS (primMinusNatS Zero ww140) (Succ ww141)",fontsize=16,color="burlywood",shape="box"];1368[label="ww140/Succ ww1400",fontsize=10,color="white",style="solid",shape="box"];1296 -> 1368[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1368 -> 1299[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1369[label="ww140/Zero",fontsize=10,color="white",style="solid",shape="box"];1296 -> 1369[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1369 -> 1300[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1138[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS (Succ ww1320) (Succ ww1330))",fontsize=16,color="black",shape="box"];1138 -> 1152[label="",style="solid", color="black", weight=3]; 30.48/16.56 1139[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS (Succ ww1320) Zero)",fontsize=16,color="black",shape="box"];1139 -> 1153[label="",style="solid", color="black", weight=3]; 30.48/16.56 1140[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS Zero (Succ ww1330))",fontsize=16,color="black",shape="box"];1140 -> 1154[label="",style="solid", color="black", weight=3]; 30.48/16.56 1141[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1141 -> 1155[label="",style="solid", color="black", weight=3]; 30.48/16.56 1205[label="primModNatS (primMinusNatS (Succ ww1350) ww136) (Succ ww137)",fontsize=16,color="burlywood",shape="box"];1370[label="ww136/Succ ww1360",fontsize=10,color="white",style="solid",shape="box"];1205 -> 1370[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1370 -> 1211[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1371[label="ww136/Zero",fontsize=10,color="white",style="solid",shape="box"];1205 -> 1371[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1371 -> 1212[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1206[label="primModNatS (primMinusNatS Zero ww136) (Succ ww137)",fontsize=16,color="burlywood",shape="box"];1372[label="ww136/Succ ww1360",fontsize=10,color="white",style="solid",shape="box"];1206 -> 1372[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1372 -> 1213[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1373[label="ww136/Zero",fontsize=10,color="white",style="solid",shape="box"];1206 -> 1373[label="",style="solid", color="burlywood", weight=9]; 30.48/16.56 1373 -> 1214[label="",style="solid", color="burlywood", weight=3]; 30.48/16.56 1142[label="ww1280",fontsize=16,color="green",shape="box"];1143[label="ww1270",fontsize=16,color="green",shape="box"];1144[label="Succ (primDivNatS (primMinusNatS (Succ ww125) (Succ ww126)) (Succ (Succ ww126)))",fontsize=16,color="green",shape="box"];1144 -> 1156[label="",style="dashed", color="green", weight=3]; 30.48/16.56 1145[label="Zero",fontsize=16,color="green",shape="box"];1297[label="primDivNatS (primMinusNatS (Succ ww1390) (Succ ww1400)) (Succ ww141)",fontsize=16,color="black",shape="box"];1297 -> 1301[label="",style="solid", color="black", weight=3]; 30.48/16.56 1298[label="primDivNatS (primMinusNatS (Succ ww1390) Zero) (Succ ww141)",fontsize=16,color="black",shape="box"];1298 -> 1302[label="",style="solid", color="black", weight=3]; 30.48/16.56 1299[label="primDivNatS (primMinusNatS Zero (Succ ww1400)) (Succ ww141)",fontsize=16,color="black",shape="box"];1299 -> 1303[label="",style="solid", color="black", weight=3]; 30.48/16.56 1300[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww141)",fontsize=16,color="black",shape="box"];1300 -> 1304[label="",style="solid", color="black", weight=3]; 30.48/16.56 1152 -> 1087[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1152[label="primModNatS0 (Succ ww130) (Succ ww131) (primGEqNatS ww1320 ww1330)",fontsize=16,color="magenta"];1152 -> 1161[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1152 -> 1162[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1153[label="primModNatS0 (Succ ww130) (Succ ww131) True",fontsize=16,color="black",shape="triangle"];1153 -> 1163[label="",style="solid", color="black", weight=3]; 30.48/16.56 1154[label="primModNatS0 (Succ ww130) (Succ ww131) False",fontsize=16,color="black",shape="box"];1154 -> 1164[label="",style="solid", color="black", weight=3]; 30.48/16.56 1155 -> 1153[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1155[label="primModNatS0 (Succ ww130) (Succ ww131) True",fontsize=16,color="magenta"];1211[label="primModNatS (primMinusNatS (Succ ww1350) (Succ ww1360)) (Succ ww137)",fontsize=16,color="black",shape="box"];1211 -> 1219[label="",style="solid", color="black", weight=3]; 30.48/16.56 1212[label="primModNatS (primMinusNatS (Succ ww1350) Zero) (Succ ww137)",fontsize=16,color="black",shape="box"];1212 -> 1220[label="",style="solid", color="black", weight=3]; 30.48/16.56 1213[label="primModNatS (primMinusNatS Zero (Succ ww1360)) (Succ ww137)",fontsize=16,color="black",shape="box"];1213 -> 1221[label="",style="solid", color="black", weight=3]; 30.48/16.56 1214[label="primModNatS (primMinusNatS Zero Zero) (Succ ww137)",fontsize=16,color="black",shape="box"];1214 -> 1222[label="",style="solid", color="black", weight=3]; 30.48/16.56 1156 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1156[label="primDivNatS (primMinusNatS (Succ ww125) (Succ ww126)) (Succ (Succ ww126))",fontsize=16,color="magenta"];1156 -> 1277[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1156 -> 1278[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1156 -> 1279[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1301 -> 1270[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1301[label="primDivNatS (primMinusNatS ww1390 ww1400) (Succ ww141)",fontsize=16,color="magenta"];1301 -> 1305[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1301 -> 1306[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1302 -> 489[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1302[label="primDivNatS (Succ ww1390) (Succ ww141)",fontsize=16,color="magenta"];1302 -> 1307[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1302 -> 1308[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1303[label="primDivNatS Zero (Succ ww141)",fontsize=16,color="black",shape="triangle"];1303 -> 1309[label="",style="solid", color="black", weight=3]; 30.48/16.56 1304 -> 1303[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1304[label="primDivNatS Zero (Succ ww141)",fontsize=16,color="magenta"];1161[label="ww1330",fontsize=16,color="green",shape="box"];1162[label="ww1320",fontsize=16,color="green",shape="box"];1163 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1163[label="primModNatS (primMinusNatS (Succ ww130) (Succ ww131)) (Succ (Succ ww131))",fontsize=16,color="magenta"];1163 -> 1187[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1163 -> 1188[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1163 -> 1189[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1164[label="Succ (Succ ww130)",fontsize=16,color="green",shape="box"];1219 -> 1174[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1219[label="primModNatS (primMinusNatS ww1350 ww1360) (Succ ww137)",fontsize=16,color="magenta"];1219 -> 1229[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1219 -> 1230[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1220 -> 495[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1220[label="primModNatS (Succ ww1350) (Succ ww137)",fontsize=16,color="magenta"];1220 -> 1231[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1220 -> 1232[label="",style="dashed", color="magenta", weight=3]; 30.48/16.56 1221[label="primModNatS Zero (Succ ww137)",fontsize=16,color="black",shape="triangle"];1221 -> 1233[label="",style="solid", color="black", weight=3]; 30.48/16.56 1222 -> 1221[label="",style="dashed", color="red", weight=0]; 30.48/16.56 1222[label="primModNatS Zero (Succ ww137)",fontsize=16,color="magenta"];1277[label="Succ ww125",fontsize=16,color="green",shape="box"];1278[label="Succ ww126",fontsize=16,color="green",shape="box"];1279[label="Succ ww126",fontsize=16,color="green",shape="box"];1305[label="ww1390",fontsize=16,color="green",shape="box"];1306[label="ww1400",fontsize=16,color="green",shape="box"];1307[label="ww1390",fontsize=16,color="green",shape="box"];1308[label="ww141",fontsize=16,color="green",shape="box"];1309[label="Zero",fontsize=16,color="green",shape="box"];1187[label="Succ ww130",fontsize=16,color="green",shape="box"];1188[label="Succ ww131",fontsize=16,color="green",shape="box"];1189[label="Succ ww131",fontsize=16,color="green",shape="box"];1229[label="ww1350",fontsize=16,color="green",shape="box"];1230[label="ww1360",fontsize=16,color="green",shape="box"];1231[label="ww1350",fontsize=16,color="green",shape="box"];1232[label="ww137",fontsize=16,color="green",shape="box"];1233[label="Zero",fontsize=16,color="green",shape="box"];} 30.48/16.56 30.48/16.56 ---------------------------------------- 30.48/16.56 30.48/16.56 (113) 30.48/16.56 TRUE 30.61/16.62 EOF