8.23/3.57 YES 10.08/4.09 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 10.08/4.09 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.08/4.09 10.08/4.09 10.08/4.09 H-Termination with start terms of the given HASKELL could be proven: 10.08/4.09 10.08/4.09 (0) HASKELL 10.08/4.09 (1) BR [EQUIVALENT, 0 ms] 10.08/4.09 (2) HASKELL 10.08/4.09 (3) COR [EQUIVALENT, 0 ms] 10.08/4.09 (4) HASKELL 10.08/4.09 (5) NumRed [SOUND, 0 ms] 10.08/4.09 (6) HASKELL 10.08/4.09 (7) Narrow [EQUIVALENT, 0 ms] 10.08/4.09 (8) YES 10.08/4.09 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (0) 10.08/4.09 Obligation: 10.08/4.09 mainModule Main 10.08/4.09 module Main where { 10.08/4.09 import qualified Prelude; 10.08/4.09 } 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (1) BR (EQUIVALENT) 10.08/4.09 Replaced joker patterns by fresh variables and removed binding patterns. 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (2) 10.08/4.09 Obligation: 10.08/4.09 mainModule Main 10.08/4.09 module Main where { 10.08/4.09 import qualified Prelude; 10.08/4.09 } 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (3) COR (EQUIVALENT) 10.08/4.09 Cond Reductions: 10.08/4.09 The following Function with conditions 10.08/4.09 "toEnum 0 = (); 10.08/4.09 " 10.08/4.09 is transformed to 10.08/4.09 "toEnum vz = toEnum1 vz; 10.08/4.09 " 10.08/4.09 "toEnum0 True vz = (); 10.08/4.09 " 10.08/4.09 "toEnum1 vz = toEnum0 (vz == 0) vz; 10.08/4.09 " 10.08/4.09 The following Function with conditions 10.08/4.09 "undefined |Falseundefined; 10.08/4.09 " 10.08/4.09 is transformed to 10.08/4.09 "undefined = undefined1; 10.08/4.09 " 10.08/4.09 "undefined0 True = undefined; 10.08/4.09 " 10.08/4.09 "undefined1 = undefined0 False; 10.08/4.09 " 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (4) 10.08/4.09 Obligation: 10.08/4.09 mainModule Main 10.08/4.09 module Main where { 10.08/4.09 import qualified Prelude; 10.08/4.09 } 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (5) NumRed (SOUND) 10.08/4.09 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (6) 10.08/4.09 Obligation: 10.08/4.09 mainModule Main 10.08/4.09 module Main where { 10.08/4.09 import qualified Prelude; 10.08/4.09 } 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (7) Narrow (EQUIVALENT) 10.08/4.09 Haskell To QDPs 10.08/4.09 10.08/4.09 digraph dp_graph { 10.08/4.09 node [outthreshold=100, inthreshold=100];1[label="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 10.08/4.09 3[label="pred wu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 10.08/4.09 4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 10.08/4.09 5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 10.08/4.09 6[label="toEnum1 ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 10.08/4.09 7[label="toEnum0 ((subtract (Pos (Succ Zero))) . fromEnum == Pos Zero) ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 10.08/4.09 8[label="toEnum0 (primEqInt ((subtract (Pos (Succ Zero))) . fromEnum) (Pos Zero)) ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 10.08/4.09 9[label="toEnum0 (primEqInt (subtract (Pos (Succ Zero)) (fromEnum wu3)) (Pos Zero)) (subtract (Pos (Succ Zero)) (fromEnum wu3))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10.08/4.09 10[label="toEnum0 (primEqInt (flip (-) (Pos (Succ Zero)) (fromEnum wu3)) (Pos Zero)) (flip (-) (Pos (Succ Zero)) (fromEnum wu3))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 10.08/4.09 11[label="toEnum0 (primEqInt ((-) fromEnum wu3 Pos (Succ Zero)) (Pos Zero)) ((-) fromEnum wu3 Pos (Succ Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 10.08/4.09 12[label="toEnum0 (primEqInt (primMinusInt (fromEnum wu3) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum wu3) (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];19[label="wu3/()",fontsize=10,color="white",style="solid",shape="box"];12 -> 19[label="",style="solid", color="burlywood", weight=9]; 10.08/4.09 19 -> 13[label="",style="solid", color="burlywood", weight=3]; 10.08/4.09 13[label="toEnum0 (primEqInt (primMinusInt (fromEnum ()) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum ()) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 10.08/4.09 14[label="toEnum0 (primEqInt (primMinusInt (Pos Zero) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos Zero) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 10.08/4.09 15[label="toEnum0 (primEqInt (primMinusNat Zero (Succ Zero)) (Pos Zero)) (primMinusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 10.08/4.09 16[label="toEnum0 (primEqInt (Neg (Succ Zero)) (Pos Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];16 -> 17[label="",style="solid", color="black", weight=3]; 10.08/4.09 17[label="toEnum0 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 10.08/4.09 18[label="error []",fontsize=16,color="red",shape="box"];} 10.08/4.09 10.08/4.09 ---------------------------------------- 10.08/4.09 10.08/4.09 (8) 10.08/4.09 YES 10.08/4.12 EOF