/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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 [SOUND, 0 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) 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 ; evenMyInt :: MyInt -> MyBool; evenMyInt = primEvenInt; not :: MyBool -> MyBool; not MyTrue = MyFalse; not MyFalse = MyTrue; oddMyInt :: MyInt -> MyBool; oddMyInt = pt not evenMyInt; primEvenInt :: MyInt -> MyBool; primEvenInt (Main.Pos x) = primEvenNat x; primEvenInt (Main.Neg x) = primEvenNat x; primEvenNat :: Main.Nat -> MyBool; primEvenNat Main.Zero = MyTrue; primEvenNat (Main.Succ Main.Zero) = MyFalse; primEvenNat (Main.Succ (Main.Succ x)) = primEvenNat x; pt :: (b -> a) -> (c -> b) -> c -> a; pt f g x = f (g x); } ---------------------------------------- (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 ; evenMyInt :: MyInt -> MyBool; evenMyInt = primEvenInt; not :: MyBool -> MyBool; not MyTrue = MyFalse; not MyFalse = MyTrue; oddMyInt :: MyInt -> MyBool; oddMyInt = pt not evenMyInt; primEvenInt :: MyInt -> MyBool; primEvenInt (Main.Pos x) = primEvenNat x; primEvenInt (Main.Neg x) = primEvenNat x; primEvenNat :: Main.Nat -> MyBool; primEvenNat Main.Zero = MyTrue; primEvenNat (Main.Succ Main.Zero) = MyFalse; primEvenNat (Main.Succ (Main.Succ x)) = primEvenNat x; pt :: (a -> b) -> (c -> a) -> c -> b; pt f g x = f (g x); } ---------------------------------------- (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 ; evenMyInt :: MyInt -> MyBool; evenMyInt = primEvenInt; not :: MyBool -> MyBool; not MyTrue = MyFalse; not MyFalse = MyTrue; oddMyInt :: MyInt -> MyBool; oddMyInt = pt not evenMyInt; primEvenInt :: MyInt -> MyBool; primEvenInt (Main.Pos x) = primEvenNat x; primEvenInt (Main.Neg x) = primEvenNat x; primEvenNat :: Main.Nat -> MyBool; primEvenNat Main.Zero = MyTrue; primEvenNat (Main.Succ Main.Zero) = MyFalse; primEvenNat (Main.Succ (Main.Succ x)) = primEvenNat x; pt :: (c -> a) -> (b -> c) -> b -> a; pt f g x = f (g x); } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="oddMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="oddMyInt vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="pt not evenMyInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="not (evenMyInt vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="not (primEvenInt vx3)",fontsize=16,color="burlywood",shape="box"];22[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 7[label="",style="solid", color="burlywood", weight=3]; 23[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 8[label="",style="solid", color="burlywood", weight=3]; 7[label="not (primEvenInt (Pos vx30))",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8[label="not (primEvenInt (Neg vx30))",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="not (primEvenNat vx30)",fontsize=16,color="burlywood",shape="triangle"];24[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];9 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 11[label="",style="solid", color="burlywood", weight=3]; 25[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 25[label="",style="solid", color="burlywood", weight=9]; 25 -> 12[label="",style="solid", color="burlywood", weight=3]; 10 -> 9[label="",style="dashed", color="red", weight=0]; 10[label="not (primEvenNat vx30)",fontsize=16,color="magenta"];10 -> 13[label="",style="dashed", color="magenta", weight=3]; 11[label="not (primEvenNat (Succ vx300))",fontsize=16,color="burlywood",shape="box"];26[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];11 -> 26[label="",style="solid", color="burlywood", weight=9]; 26 -> 14[label="",style="solid", color="burlywood", weight=3]; 27[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];11 -> 27[label="",style="solid", color="burlywood", weight=9]; 27 -> 15[label="",style="solid", color="burlywood", weight=3]; 12[label="not (primEvenNat Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 13[label="vx30",fontsize=16,color="green",shape="box"];14[label="not (primEvenNat (Succ (Succ vx3000)))",fontsize=16,color="black",shape="box"];14 -> 17[label="",style="solid", color="black", weight=3]; 15[label="not (primEvenNat (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3]; 16[label="not MyTrue",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3]; 17 -> 9[label="",style="dashed", color="red", weight=0]; 17[label="not (primEvenNat vx3000)",fontsize=16,color="magenta"];17 -> 20[label="",style="dashed", color="magenta", weight=3]; 18[label="not MyFalse",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3]; 19[label="MyFalse",fontsize=16,color="green",shape="box"];20[label="vx3000",fontsize=16,color="green",shape="box"];21[label="MyTrue",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_not(Main.Succ(Main.Succ(vx3000))) -> new_not(vx3000) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_not(Main.Succ(Main.Succ(vx3000))) -> new_not(vx3000) The graph contains the following edges 1 > 1 ---------------------------------------- (8) YES