7.58/3.75 YES 9.33/4.25 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.33/4.25 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.33/4.25 9.33/4.25 9.33/4.25 H-Termination with start terms of the given HASKELL could be proven: 9.33/4.25 9.33/4.25 (0) HASKELL 9.33/4.25 (1) BR [EQUIVALENT, 0 ms] 9.33/4.25 (2) HASKELL 9.33/4.25 (3) COR [EQUIVALENT, 0 ms] 9.33/4.25 (4) HASKELL 9.33/4.25 (5) Narrow [EQUIVALENT, 30 ms] 9.33/4.25 (6) YES 9.33/4.25 9.33/4.25 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (0) 9.33/4.25 Obligation: 9.33/4.25 mainModule Main 9.33/4.25 module Main where { 9.33/4.25 import qualified Prelude; 9.33/4.25 data MyBool = MyTrue | MyFalse ; 9.33/4.25 9.33/4.25 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.33/4.25 9.33/4.25 data Main.Nat = Succ Main.Nat | Zero ; 9.33/4.25 9.33/4.25 data Tup0 = Tup0 ; 9.33/4.25 9.33/4.25 esEsMyInt :: MyInt -> MyInt -> MyBool; 9.33/4.25 esEsMyInt = primEqInt; 9.33/4.25 9.33/4.25 primEqInt :: MyInt -> MyInt -> MyBool; 9.33/4.25 primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; 9.33/4.25 primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; 9.33/4.25 primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; 9.33/4.25 primEqInt vv vw = MyFalse; 9.33/4.25 9.33/4.25 primEqNat :: Main.Nat -> Main.Nat -> MyBool; 9.33/4.25 primEqNat Main.Zero Main.Zero = MyTrue; 9.33/4.25 primEqNat Main.Zero (Main.Succ y) = MyFalse; 9.33/4.25 primEqNat (Main.Succ x) Main.Zero = MyFalse; 9.33/4.25 primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; 9.33/4.25 9.33/4.25 toEnum0 MyTrue vx = Tup0; 9.33/4.25 9.33/4.25 toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx; 9.33/4.25 9.33/4.25 toEnumTup0 :: MyInt -> Tup0; 9.33/4.25 toEnumTup0 vx = toEnum1 vx; 9.33/4.25 9.33/4.25 } 9.33/4.25 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (1) BR (EQUIVALENT) 9.33/4.25 Replaced joker patterns by fresh variables and removed binding patterns. 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (2) 9.33/4.25 Obligation: 9.33/4.25 mainModule Main 9.33/4.25 module Main where { 9.33/4.25 import qualified Prelude; 9.33/4.25 data MyBool = MyTrue | MyFalse ; 9.33/4.25 9.33/4.25 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.33/4.25 9.33/4.25 data Main.Nat = Succ Main.Nat | Zero ; 9.33/4.25 9.33/4.25 data Tup0 = Tup0 ; 9.33/4.25 9.33/4.25 esEsMyInt :: MyInt -> MyInt -> MyBool; 9.33/4.25 esEsMyInt = primEqInt; 9.33/4.25 9.33/4.25 primEqInt :: MyInt -> MyInt -> MyBool; 9.33/4.25 primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; 9.33/4.25 primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; 9.33/4.25 primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; 9.33/4.25 primEqInt vv vw = MyFalse; 9.33/4.25 9.33/4.25 primEqNat :: Main.Nat -> Main.Nat -> MyBool; 9.33/4.25 primEqNat Main.Zero Main.Zero = MyTrue; 9.33/4.25 primEqNat Main.Zero (Main.Succ y) = MyFalse; 9.33/4.25 primEqNat (Main.Succ x) Main.Zero = MyFalse; 9.33/4.25 primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; 9.33/4.25 9.33/4.25 toEnum0 MyTrue vx = Tup0; 9.33/4.25 9.33/4.25 toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx; 9.33/4.25 9.33/4.25 toEnumTup0 :: MyInt -> Tup0; 9.33/4.25 toEnumTup0 vx = toEnum1 vx; 9.33/4.25 9.33/4.25 } 9.33/4.25 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (3) COR (EQUIVALENT) 9.33/4.25 Cond Reductions: 9.33/4.25 The following Function with conditions 9.33/4.25 "undefined |Falseundefined; 9.33/4.25 " 9.33/4.25 is transformed to 9.33/4.25 "undefined = undefined1; 9.33/4.25 " 9.33/4.25 "undefined0 True = undefined; 9.33/4.25 " 9.33/4.25 "undefined1 = undefined0 False; 9.33/4.25 " 9.33/4.25 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (4) 9.33/4.25 Obligation: 9.33/4.25 mainModule Main 9.33/4.25 module Main where { 9.33/4.25 import qualified Prelude; 9.33/4.25 data MyBool = MyTrue | MyFalse ; 9.33/4.25 9.33/4.25 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.33/4.25 9.33/4.25 data Main.Nat = Succ Main.Nat | Zero ; 9.33/4.25 9.33/4.25 data Tup0 = Tup0 ; 9.33/4.25 9.33/4.25 esEsMyInt :: MyInt -> MyInt -> MyBool; 9.33/4.25 esEsMyInt = primEqInt; 9.33/4.25 9.33/4.25 primEqInt :: MyInt -> MyInt -> MyBool; 9.33/4.25 primEqInt (Main.Pos (Main.Succ x)) (Main.Pos (Main.Succ y)) = primEqNat x y; 9.33/4.25 primEqInt (Main.Neg (Main.Succ x)) (Main.Neg (Main.Succ y)) = primEqNat x y; 9.33/4.25 primEqInt (Main.Pos Main.Zero) (Main.Neg Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Neg Main.Zero) (Main.Pos Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Neg Main.Zero) (Main.Neg Main.Zero) = MyTrue; 9.33/4.25 primEqInt (Main.Pos Main.Zero) (Main.Pos Main.Zero) = MyTrue; 9.33/4.25 primEqInt vv vw = MyFalse; 9.33/4.25 9.33/4.25 primEqNat :: Main.Nat -> Main.Nat -> MyBool; 9.33/4.25 primEqNat Main.Zero Main.Zero = MyTrue; 9.33/4.25 primEqNat Main.Zero (Main.Succ y) = MyFalse; 9.33/4.25 primEqNat (Main.Succ x) Main.Zero = MyFalse; 9.33/4.25 primEqNat (Main.Succ x) (Main.Succ y) = primEqNat x y; 9.33/4.25 9.33/4.25 toEnum0 MyTrue vx = Tup0; 9.33/4.25 9.33/4.25 toEnum1 vx = toEnum0 (esEsMyInt vx (Main.Pos Main.Zero)) vx; 9.33/4.25 9.33/4.25 toEnumTup0 :: MyInt -> Tup0; 9.33/4.25 toEnumTup0 vx = toEnum1 vx; 9.33/4.25 9.33/4.25 } 9.33/4.25 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (5) Narrow (EQUIVALENT) 9.33/4.25 Haskell To QDPs 9.33/4.25 9.33/4.25 digraph dp_graph { 9.33/4.25 node [outthreshold=100, inthreshold=100];1[label="toEnumTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.33/4.25 3[label="toEnumTup0 wu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.33/4.25 4[label="toEnum1 wu3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.33/4.25 5[label="toEnum0 (esEsMyInt wu3 (Pos Zero)) wu3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.33/4.25 6[label="toEnum0 (primEqInt wu3 (Pos Zero)) wu3",fontsize=16,color="burlywood",shape="box"];21[label="wu3/Pos wu30",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9]; 9.33/4.25 21 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.33/4.25 22[label="wu3/Neg wu30",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9]; 9.33/4.25 22 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.33/4.25 7[label="toEnum0 (primEqInt (Pos wu30) (Pos Zero)) (Pos wu30)",fontsize=16,color="burlywood",shape="box"];23[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];7 -> 23[label="",style="solid", color="burlywood", weight=9]; 9.33/4.25 23 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.33/4.25 24[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 24[label="",style="solid", color="burlywood", weight=9]; 9.33/4.25 24 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.33/4.25 8[label="toEnum0 (primEqInt (Neg wu30) (Pos Zero)) (Neg wu30)",fontsize=16,color="burlywood",shape="box"];25[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];8 -> 25[label="",style="solid", color="burlywood", weight=9]; 9.33/4.25 25 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.33/4.25 26[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 26[label="",style="solid", color="burlywood", weight=9]; 9.33/4.25 26 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.33/4.25 9[label="toEnum0 (primEqInt (Pos (Succ wu300)) (Pos Zero)) (Pos (Succ wu300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 9.33/4.25 10[label="toEnum0 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 9.33/4.25 11[label="toEnum0 (primEqInt (Neg (Succ wu300)) (Pos Zero)) (Neg (Succ wu300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 9.33/4.25 12[label="toEnum0 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 9.33/4.25 13[label="toEnum0 MyFalse (Pos (Succ wu300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 9.33/4.25 14[label="toEnum0 MyTrue (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 9.33/4.25 15[label="toEnum0 MyFalse (Neg (Succ wu300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 9.33/4.25 16[label="toEnum0 MyTrue (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 9.33/4.25 17[label="error []",fontsize=16,color="red",shape="box"];18[label="Tup0",fontsize=16,color="green",shape="box"];19[label="error []",fontsize=16,color="red",shape="box"];20[label="Tup0",fontsize=16,color="green",shape="box"];} 9.33/4.25 9.33/4.25 ---------------------------------------- 9.33/4.25 9.33/4.25 (6) 9.33/4.25 YES 9.42/4.29 EOF