/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) Narrow [EQUIVALENT, 28 ms] (6) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; data MyBool = MyTrue | MyFalse ; data MyInt = Pos Main.Nat | Neg Main.Nat ; data Main.Nat = Succ Main.Nat | Zero ; esEsMyInt :: MyInt -> MyInt -> MyBool; esEsMyInt = primEqInt; primEqInt :: MyInt -> MyInt -> MyBool; primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; primEqInt vv vw = MyFalse; primEqNat :: Main.Nat -> Main.Nat -> MyBool; primEqNat Main.Zero Main.Zero = MyTrue; primEqNat Main.Zero (Main.Succ y) = MyFalse; primEqNat (Main.Succ x) Main.Zero = MyFalse; primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; toEnum0 MyTrue vx = MyTrue; toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos (Main.Succ Main.Zero))) vx; toEnum2 MyTrue vy = MyFalse; toEnum2 vz wu = toEnum1 wu; toEnum3 vy = toEnum2 (esEsMyInt vy (Main.Pos Main.Zero)) vy; toEnum3 wv = toEnum1 wv; toEnumMyBool :: MyInt -> MyBool; toEnumMyBool vy = toEnum3 vy; toEnumMyBool vx = toEnum1 vx; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; data MyBool = MyTrue | MyFalse ; data MyInt = Pos Main.Nat | Neg Main.Nat ; data Main.Nat = Succ Main.Nat | Zero ; esEsMyInt :: MyInt -> MyInt -> MyBool; esEsMyInt = primEqInt; primEqInt :: MyInt -> MyInt -> MyBool; primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; primEqInt vv vw = MyFalse; primEqNat :: Main.Nat -> Main.Nat -> MyBool; primEqNat Main.Zero Main.Zero = MyTrue; primEqNat Main.Zero (Main.Succ y) = MyFalse; primEqNat (Main.Succ x) Main.Zero = MyFalse; primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; toEnum0 MyTrue vx = MyTrue; toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos (Main.Succ Main.Zero))) vx; toEnum2 MyTrue vy = MyFalse; toEnum2 vz wu = toEnum1 wu; toEnum3 vy = toEnum2 (esEsMyInt vy (Main.Pos Main.Zero)) vy; toEnum3 wv = toEnum1 wv; toEnumMyBool :: MyInt -> MyBool; toEnumMyBool vy = toEnum3 vy; toEnumMyBool vx = toEnum1 vx; } ---------------------------------------- (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; data MyBool = MyTrue | MyFalse ; data MyInt = Pos Main.Nat | Neg Main.Nat ; data Main.Nat = Succ Main.Nat | Zero ; esEsMyInt :: MyInt -> MyInt -> MyBool; esEsMyInt = primEqInt; primEqInt :: MyInt -> MyInt -> MyBool; primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; primEqInt vv vw = MyFalse; primEqNat :: Main.Nat -> Main.Nat -> MyBool; primEqNat Main.Zero Main.Zero = MyTrue; primEqNat Main.Zero (Main.Succ y) = MyFalse; primEqNat (Main.Succ x) Main.Zero = MyFalse; primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; toEnum0 MyTrue vx = MyTrue; toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos (Main.Succ Main.Zero))) vx; toEnum2 MyTrue vy = MyFalse; toEnum2 vz wu = toEnum1 wu; toEnum3 vy = toEnum2 (esEsMyInt vy (Main.Pos Main.Zero)) vy; toEnum3 wv = toEnum1 wv; toEnumMyBool :: MyInt -> MyBool; toEnumMyBool vy = toEnum3 vy; toEnumMyBool vx = toEnum1 vx; } ---------------------------------------- (5) Narrow (EQUIVALENT) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="toEnumMyBool",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="toEnumMyBool wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="toEnum3 wy3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="toEnum2 (esEsMyInt wy3 (Pos Zero)) wy3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="toEnum2 (primEqInt wy3 (Pos Zero)) wy3",fontsize=16,color="burlywood",shape="box"];34[label="wy3/Pos wy30",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9]; 34 -> 7[label="",style="solid", color="burlywood", weight=3]; 35[label="wy3/Neg wy30",fontsize=10,color="white",style="solid",shape="box"];6 -> 35[label="",style="solid", color="burlywood", weight=9]; 35 -> 8[label="",style="solid", color="burlywood", weight=3]; 7[label="toEnum2 (primEqInt (Pos wy30) (Pos Zero)) (Pos wy30)",fontsize=16,color="burlywood",shape="box"];36[label="wy30/Succ wy300",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9]; 36 -> 9[label="",style="solid", color="burlywood", weight=3]; 37[label="wy30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9]; 37 -> 10[label="",style="solid", color="burlywood", weight=3]; 8[label="toEnum2 (primEqInt (Neg wy30) (Pos Zero)) (Neg wy30)",fontsize=16,color="burlywood",shape="box"];38[label="wy30/Succ wy300",fontsize=10,color="white",style="solid",shape="box"];8 -> 38[label="",style="solid", color="burlywood", weight=9]; 38 -> 11[label="",style="solid", color="burlywood", weight=3]; 39[label="wy30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 39[label="",style="solid", color="burlywood", weight=9]; 39 -> 12[label="",style="solid", color="burlywood", weight=3]; 9[label="toEnum2 (primEqInt (Pos (Succ wy300)) (Pos Zero)) (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 10[label="toEnum2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 11[label="toEnum2 (primEqInt (Neg (Succ wy300)) (Pos Zero)) (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 12[label="toEnum2 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 13[label="toEnum2 MyFalse (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 14[label="toEnum2 MyTrue (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 15[label="toEnum2 MyFalse (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 16[label="toEnum2 MyTrue (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 17[label="toEnum1 (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 18[label="MyFalse",fontsize=16,color="green",shape="box"];19[label="toEnum1 (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3]; 20[label="MyFalse",fontsize=16,color="green",shape="box"];21[label="toEnum0 (esEsMyInt (Pos (Succ wy300)) (Pos (Succ Zero))) (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3]; 22[label="toEnum0 (esEsMyInt (Neg (Succ wy300)) (Pos (Succ Zero))) (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3]; 23[label="toEnum0 (primEqInt (Pos (Succ wy300)) (Pos (Succ Zero))) (Pos (Succ wy300))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3]; 24[label="toEnum0 (primEqInt (Neg (Succ wy300)) (Pos (Succ Zero))) (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3]; 25[label="toEnum0 (primEqNat wy300 Zero) (Pos (Succ wy300))",fontsize=16,color="burlywood",shape="box"];40[label="wy300/Succ wy3000",fontsize=10,color="white",style="solid",shape="box"];25 -> 40[label="",style="solid", color="burlywood", weight=9]; 40 -> 27[label="",style="solid", color="burlywood", weight=3]; 41[label="wy300/Zero",fontsize=10,color="white",style="solid",shape="box"];25 -> 41[label="",style="solid", color="burlywood", weight=9]; 41 -> 28[label="",style="solid", color="burlywood", weight=3]; 26[label="toEnum0 MyFalse (Neg (Succ wy300))",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3]; 27[label="toEnum0 (primEqNat (Succ wy3000) Zero) (Pos (Succ (Succ wy3000)))",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3]; 28[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3]; 29[label="error []",fontsize=16,color="red",shape="box"];30[label="toEnum0 MyFalse (Pos (Succ (Succ wy3000)))",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3]; 31[label="toEnum0 MyTrue (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 33[label="",style="solid", color="black", weight=3]; 32[label="error []",fontsize=16,color="red",shape="box"];33[label="MyTrue",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) YES