/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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, 11 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; " ---------------------------------------- (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="recip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="recip vx3",fontsize=16,color="blue",shape="box"];42[label="recip :: (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 42[label="",style="solid", color="blue", weight=9]; 42 -> 4[label="",style="solid", color="blue", weight=3]; 43[label="recip :: Double -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 43[label="",style="solid", color="blue", weight=9]; 43 -> 5[label="",style="solid", color="blue", weight=3]; 44[label="recip :: Float -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 44[label="",style="solid", color="blue", weight=9]; 44 -> 6[label="",style="solid", color="blue", weight=3]; 4[label="recip vx3",fontsize=16,color="burlywood",shape="box"];45[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 7[label="",style="solid", color="burlywood", weight=3]; 5[label="recip vx3",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3]; 6[label="recip vx3",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3]; 7[label="recip (vx30 :% vx31)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3]; 8[label="fromInt (Pos (Succ Zero)) / vx3",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 9[label="fromInt (Pos (Succ Zero)) / vx3",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3]; 10[label="vx31 :% vx30",fontsize=16,color="green",shape="box"];11[label="primDivDouble (fromInt (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="primDivFloat (fromInt (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="primDivDouble (primIntToDouble (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="primDivFloat (primIntToFloat (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="primDivDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];46[label="vx3/Double vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];15 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 17[label="",style="solid", color="burlywood", weight=3]; 16[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];47[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];16 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 18[label="",style="solid", color="burlywood", weight=3]; 17[label="primDivDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) (Double vx30 vx31)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vx30 vx31)",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="Double (Pos (Succ Zero) * vx31) (Pos (Succ Zero) * vx30)",fontsize=16,color="green",shape="box"];19 -> 21[label="",style="dashed", color="green", weight=3]; 19 -> 22[label="",style="dashed", color="green", weight=3]; 20[label="Float (Pos (Succ Zero) * vx31) (Pos (Succ Zero) * vx30)",fontsize=16,color="green",shape="box"];20 -> 23[label="",style="dashed", color="green", weight=3]; 20 -> 24[label="",style="dashed", color="green", weight=3]; 21[label="Pos (Succ Zero) * vx31",fontsize=16,color="black",shape="triangle"];21 -> 25[label="",style="solid", color="black", weight=3]; 22 -> 21[label="",style="dashed", color="red", weight=0]; 22[label="Pos (Succ Zero) * vx30",fontsize=16,color="magenta"];22 -> 26[label="",style="dashed", color="magenta", weight=3]; 23 -> 21[label="",style="dashed", color="red", weight=0]; 23[label="Pos (Succ Zero) * vx31",fontsize=16,color="magenta"];23 -> 27[label="",style="dashed", color="magenta", weight=3]; 24 -> 21[label="",style="dashed", color="red", weight=0]; 24[label="Pos (Succ Zero) * vx30",fontsize=16,color="magenta"];24 -> 28[label="",style="dashed", color="magenta", weight=3]; 25[label="primMulInt (Pos (Succ Zero)) vx31",fontsize=16,color="burlywood",shape="box"];48[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];25 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 29[label="",style="solid", color="burlywood", weight=3]; 49[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];25 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 30[label="",style="solid", color="burlywood", weight=3]; 26[label="vx30",fontsize=16,color="green",shape="box"];27[label="vx31",fontsize=16,color="green",shape="box"];28[label="vx30",fontsize=16,color="green",shape="box"];29[label="primMulInt (Pos (Succ Zero)) (Pos vx310)",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3]; 30[label="primMulInt (Pos (Succ Zero)) (Neg vx310)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3]; 31[label="Pos (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];31 -> 33[label="",style="dashed", color="green", weight=3]; 32[label="Neg (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];32 -> 34[label="",style="dashed", color="green", weight=3]; 33[label="primMulNat (Succ Zero) vx310",fontsize=16,color="burlywood",shape="triangle"];50[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];33 -> 50[label="",style="solid", color="burlywood", weight=9]; 50 -> 35[label="",style="solid", color="burlywood", weight=3]; 51[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 51[label="",style="solid", color="burlywood", weight=9]; 51 -> 36[label="",style="solid", color="burlywood", weight=3]; 34 -> 33[label="",style="dashed", color="red", weight=0]; 34[label="primMulNat (Succ Zero) vx310",fontsize=16,color="magenta"];34 -> 37[label="",style="dashed", color="magenta", weight=3]; 35[label="primMulNat (Succ Zero) (Succ vx3100)",fontsize=16,color="black",shape="box"];35 -> 38[label="",style="solid", color="black", weight=3]; 36[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];36 -> 39[label="",style="solid", color="black", weight=3]; 37[label="vx310",fontsize=16,color="green",shape="box"];38[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3]; 39[label="Zero",fontsize=16,color="green",shape="box"];40[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3]; 41[label="Succ vx3100",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) YES