/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) NumRed [SOUND, 0 ms] (6) HASKELL (7) Narrow [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " The following Function with conditions "toEnum 0 = False; toEnum 1 = True; " is transformed to "toEnum wu = toEnum3 wu; toEnum vz = toEnum1 vz; " "toEnum0 True vz = True; " "toEnum1 vz = toEnum0 (vz == 1) vz; " "toEnum2 True wu = False; toEnum2 wv ww = toEnum1 ww; " "toEnum3 wu = toEnum2 (wu == 0) wu; toEnum3 wx = toEnum1 wx; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) Narrow (EQUIVALENT) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="pred wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="toEnum3 ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="toEnum2 ((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]; 8[label="toEnum2 (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]; 9[label="toEnum2 (primEqInt (subtract (Pos (Succ Zero)) (fromEnum wy3)) (Pos Zero)) (subtract (Pos (Succ Zero)) (fromEnum wy3))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3]; 10[label="toEnum2 (primEqInt (flip (-) (Pos (Succ Zero)) (fromEnum wy3)) (Pos Zero)) (flip (-) (Pos (Succ Zero)) (fromEnum wy3))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 11[label="toEnum2 (primEqInt ((-) fromEnum wy3 Pos (Succ Zero)) (Pos Zero)) ((-) fromEnum wy3 Pos (Succ Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 12[label="toEnum2 (primEqInt (primMinusInt (fromEnum wy3) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum wy3) (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];30[label="wy3/False",fontsize=10,color="white",style="solid",shape="box"];12 -> 30[label="",style="solid", color="burlywood", weight=9]; 30 -> 13[label="",style="solid", color="burlywood", weight=3]; 31[label="wy3/True",fontsize=10,color="white",style="solid",shape="box"];12 -> 31[label="",style="solid", color="burlywood", weight=9]; 31 -> 14[label="",style="solid", color="burlywood", weight=3]; 13[label="toEnum2 (primEqInt (primMinusInt (fromEnum False) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum False) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="toEnum2 (primEqInt (primMinusInt (fromEnum True) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum True) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="toEnum2 (primEqInt (primMinusInt (Pos Zero) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos Zero) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="toEnum2 (primEqInt (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="toEnum2 (primEqInt (primMinusNat Zero (Succ Zero)) (Pos Zero)) (primMinusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="toEnum2 (primEqInt (primMinusNat (Succ Zero) (Succ Zero)) (Pos Zero)) (primMinusNat (Succ Zero) (Succ Zero))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="toEnum2 (primEqInt (Neg (Succ Zero)) (Pos Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="toEnum2 (primEqInt (primMinusNat Zero Zero) (Pos Zero)) (primMinusNat Zero Zero)",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3]; 21[label="toEnum2 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 22[label="toEnum2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 23[label="toEnum1 (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 24[label="toEnum2 True (Pos Zero)",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3]; 25[label="toEnum0 (Neg (Succ Zero) == Pos (Succ Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3]; 26[label="False",fontsize=16,color="green",shape="box"];27[label="toEnum0 (primEqInt (Neg (Succ Zero)) (Pos (Succ Zero))) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3]; 28[label="toEnum0 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3]; 29[label="error []",fontsize=16,color="red",shape="box"];} ---------------------------------------- (8) YES