7.83/3.49 YES 9.40/3.97 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.40/3.97 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.40/3.97 9.40/3.97 9.40/3.97 H-Termination with start terms of the given HASKELL could be proven: 9.40/3.97 9.40/3.97 (0) HASKELL 9.40/3.97 (1) BR [EQUIVALENT, 0 ms] 9.40/3.97 (2) HASKELL 9.40/3.97 (3) COR [EQUIVALENT, 0 ms] 9.40/3.97 (4) HASKELL 9.40/3.97 (5) NumRed [SOUND, 0 ms] 9.40/3.97 (6) HASKELL 9.40/3.97 (7) Narrow [EQUIVALENT, 13 ms] 9.40/3.97 (8) YES 9.40/3.97 9.40/3.97 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (0) 9.40/3.97 Obligation: 9.40/3.97 mainModule Main 9.40/3.97 module Main where { 9.40/3.97 import qualified Prelude; 9.40/3.97 } 9.40/3.97 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (1) BR (EQUIVALENT) 9.40/3.97 Replaced joker patterns by fresh variables and removed binding patterns. 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (2) 9.40/3.97 Obligation: 9.40/3.97 mainModule Main 9.40/3.97 module Main where { 9.40/3.97 import qualified Prelude; 9.40/3.97 } 9.40/3.97 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (3) COR (EQUIVALENT) 9.40/3.97 Cond Reductions: 9.40/3.97 The following Function with conditions 9.40/3.97 "toEnum 0 = LT; 9.40/3.97 toEnum 1 = EQ; 9.40/3.97 toEnum 2 = GT; 9.40/3.97 " 9.40/3.97 is transformed to 9.40/3.97 "toEnum wy = toEnum5 wy; 9.40/3.97 toEnum wu = toEnum3 wu; 9.40/3.97 toEnum vz = toEnum1 vz; 9.40/3.97 " 9.40/3.97 "toEnum0 True vz = GT; 9.40/3.97 " 9.40/3.97 "toEnum1 vz = toEnum0 (vz == 2) vz; 9.40/3.97 " 9.40/3.97 "toEnum2 True wu = EQ; 9.40/3.97 toEnum2 wv ww = toEnum1 ww; 9.40/3.97 " 9.40/3.97 "toEnum3 wu = toEnum2 (wu == 1) wu; 9.40/3.97 toEnum3 wx = toEnum1 wx; 9.40/3.97 " 9.40/3.97 "toEnum4 True wy = LT; 9.40/3.97 toEnum4 wz xu = toEnum3 xu; 9.40/3.97 " 9.40/3.97 "toEnum5 wy = toEnum4 (wy == 0) wy; 9.40/3.97 toEnum5 xv = toEnum3 xv; 9.40/3.97 " 9.40/3.97 The following Function with conditions 9.40/3.97 "undefined |Falseundefined; 9.40/3.97 " 9.40/3.97 is transformed to 9.40/3.97 "undefined = undefined1; 9.40/3.97 " 9.40/3.97 "undefined0 True = undefined; 9.40/3.97 " 9.40/3.97 "undefined1 = undefined0 False; 9.40/3.97 " 9.40/3.97 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (4) 9.40/3.97 Obligation: 9.40/3.97 mainModule Main 9.40/3.97 module Main where { 9.40/3.97 import qualified Prelude; 9.40/3.97 } 9.40/3.97 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (5) NumRed (SOUND) 9.40/3.97 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (6) 9.40/3.97 Obligation: 9.40/3.97 mainModule Main 9.40/3.97 module Main where { 9.40/3.97 import qualified Prelude; 9.40/3.97 } 9.40/3.97 9.40/3.97 ---------------------------------------- 9.40/3.97 9.40/3.97 (7) Narrow (EQUIVALENT) 9.40/3.97 Haskell To QDPs 9.40/3.97 9.40/3.97 digraph dp_graph { 9.40/3.97 node [outthreshold=100, inthreshold=100];1[label="toEnum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.40/3.97 3[label="toEnum xw3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.40/3.97 4[label="toEnum5 xw3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.40/3.97 5[label="toEnum4 (xw3 == Pos Zero) xw3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.40/3.97 6[label="toEnum4 (primEqInt xw3 (Pos Zero)) xw3",fontsize=16,color="burlywood",shape="box"];48[label="xw3/Pos xw30",fontsize=10,color="white",style="solid",shape="box"];6 -> 48[label="",style="solid", color="burlywood", weight=9]; 9.40/3.97 48 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.40/3.97 49[label="xw3/Neg xw30",fontsize=10,color="white",style="solid",shape="box"];6 -> 49[label="",style="solid", color="burlywood", weight=9]; 9.40/3.97 49 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.40/3.97 7[label="toEnum4 (primEqInt (Pos xw30) (Pos Zero)) (Pos xw30)",fontsize=16,color="burlywood",shape="box"];50[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];7 -> 50[label="",style="solid", color="burlywood", weight=9]; 9.40/3.97 50 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.40/3.97 51[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 51[label="",style="solid", color="burlywood", weight=9]; 9.40/3.97 51 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.40/3.97 8[label="toEnum4 (primEqInt (Neg xw30) (Pos Zero)) (Neg xw30)",fontsize=16,color="burlywood",shape="box"];52[label="xw30/Succ xw300",fontsize=10,color="white",style="solid",shape="box"];8 -> 52[label="",style="solid", color="burlywood", weight=9]; 9.40/3.97 52 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.40/3.97 53[label="xw30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 53[label="",style="solid", color="burlywood", weight=9]; 9.40/3.97 53 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.40/3.97 9[label="toEnum4 (primEqInt (Pos (Succ xw300)) (Pos Zero)) (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 9.40/3.97 10[label="toEnum4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 9.40/3.97 11[label="toEnum4 (primEqInt (Neg (Succ xw300)) (Pos Zero)) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 9.40/3.97 12[label="toEnum4 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 9.40/3.97 13[label="toEnum4 False (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 9.40/3.97 14[label="toEnum4 True (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 9.40/3.97 15[label="toEnum4 False (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 9.40/3.98 16[label="toEnum4 True (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 9.40/3.98 17[label="toEnum3 (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 9.40/3.98 18[label="LT",fontsize=16,color="green",shape="box"];19[label="toEnum3 (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3]; 9.40/3.98 20[label="LT",fontsize=16,color="green",shape="box"];21[label="toEnum2 (Pos (Succ xw300) == Pos (Succ Zero)) (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 9.40/3.98 22[label="toEnum2 (Neg (Succ xw300) == Pos (Succ Zero)) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 9.40/3.98 23[label="toEnum2 (primEqInt (Pos (Succ xw300)) (Pos (Succ Zero))) (Pos (Succ xw300))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 9.40/3.98 24[label="toEnum2 (primEqInt (Neg (Succ xw300)) (Pos (Succ Zero))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3]; 9.40/3.98 25[label="toEnum2 (primEqNat xw300 Zero) (Pos (Succ xw300))",fontsize=16,color="burlywood",shape="box"];54[label="xw300/Succ xw3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 54[label="",style="solid", color="burlywood", weight=9]; 9.40/3.98 54 -> 27[label="",style="solid", color="burlywood", weight=3]; 9.40/3.98 55[label="xw300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 55[label="",style="solid", color="burlywood", weight=9]; 9.40/3.98 55 -> 28[label="",style="solid", color="burlywood", weight=3]; 9.40/3.98 26[label="toEnum2 False (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3]; 9.40/3.98 27[label="toEnum2 (primEqNat (Succ xw3000) Zero) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3]; 9.40/3.98 28[label="toEnum2 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3]; 9.40/3.98 29[label="toEnum1 (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];29 -> 32[label="",style="solid", color="black", weight=3]; 9.40/3.98 30[label="toEnum2 False (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];30 -> 33[label="",style="solid", color="black", weight=3]; 9.40/3.98 31[label="toEnum2 True (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3]; 9.40/3.98 32[label="toEnum0 (Neg (Succ xw300) == Pos (Succ (Succ Zero))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];32 -> 35[label="",style="solid", color="black", weight=3]; 9.40/3.98 33[label="toEnum1 (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];33 -> 36[label="",style="solid", color="black", weight=3]; 9.40/3.98 34[label="EQ",fontsize=16,color="green",shape="box"];35[label="toEnum0 (primEqInt (Neg (Succ xw300)) (Pos (Succ (Succ Zero)))) (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3]; 9.40/3.98 36[label="toEnum0 (Pos (Succ (Succ xw3000)) == Pos (Succ (Succ Zero))) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3]; 9.40/3.98 37[label="toEnum0 False (Neg (Succ xw300))",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3]; 9.40/3.98 38[label="toEnum0 (primEqInt (Pos (Succ (Succ xw3000))) (Pos (Succ (Succ Zero)))) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3]; 9.40/3.98 39[label="error []",fontsize=16,color="red",shape="box"];40[label="toEnum0 (primEqNat (Succ xw3000) (Succ Zero)) (Pos (Succ (Succ xw3000)))",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3]; 9.40/3.98 41[label="toEnum0 (primEqNat xw3000 Zero) (Pos (Succ (Succ xw3000)))",fontsize=16,color="burlywood",shape="box"];56[label="xw3000/Succ xw30000",fontsize=10,color="white",style="solid",shape="box"];41 -> 56[label="",style="solid", color="burlywood", weight=9]; 9.40/3.98 56 -> 42[label="",style="solid", color="burlywood", weight=3]; 9.40/3.98 57[label="xw3000/Zero",fontsize=10,color="white",style="solid",shape="box"];41 -> 57[label="",style="solid", color="burlywood", weight=9]; 9.40/3.98 57 -> 43[label="",style="solid", color="burlywood", weight=3]; 9.40/3.98 42[label="toEnum0 (primEqNat (Succ xw30000) Zero) (Pos (Succ (Succ (Succ xw30000))))",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3]; 9.40/3.98 43[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];43 -> 45[label="",style="solid", color="black", weight=3]; 9.40/3.98 44[label="toEnum0 False (Pos (Succ (Succ (Succ xw30000))))",fontsize=16,color="black",shape="box"];44 -> 46[label="",style="solid", color="black", weight=3]; 9.40/3.98 45[label="toEnum0 True (Pos (Succ (Succ Zero)))",fontsize=16,color="black",shape="box"];45 -> 47[label="",style="solid", color="black", weight=3]; 9.40/3.98 46[label="error []",fontsize=16,color="red",shape="box"];47[label="GT",fontsize=16,color="green",shape="box"];} 9.40/3.98 9.40/3.98 ---------------------------------------- 9.40/3.98 9.40/3.98 (8) 9.40/3.98 YES 9.68/4.02 EOF