/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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; 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; } ---------------------------------------- (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; 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; } ---------------------------------------- (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; 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; } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="evenMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="evenMyInt vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="primEvenInt vx3",fontsize=16,color="burlywood",shape="box"];18[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 18[label="",style="solid", color="burlywood", weight=9]; 18 -> 5[label="",style="solid", color="burlywood", weight=3]; 19[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 19[label="",style="solid", color="burlywood", weight=9]; 19 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="primEvenInt (Pos vx30)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="primEvenInt (Neg vx30)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="primEvenNat vx30",fontsize=16,color="burlywood",shape="triangle"];20[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];7 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 9[label="",style="solid", color="burlywood", weight=3]; 21[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 10[label="",style="solid", color="burlywood", weight=3]; 8 -> 7[label="",style="dashed", color="red", weight=0]; 8[label="primEvenNat vx30",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="primEvenNat (Succ vx300)",fontsize=16,color="burlywood",shape="box"];22[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];9 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 12[label="",style="solid", color="burlywood", weight=3]; 23[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];9 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 13[label="",style="solid", color="burlywood", weight=3]; 10[label="primEvenNat Zero",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 11[label="vx30",fontsize=16,color="green",shape="box"];12[label="primEvenNat (Succ (Succ vx3000))",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3]; 13[label="primEvenNat (Succ Zero)",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3]; 14[label="MyTrue",fontsize=16,color="green",shape="box"];15 -> 7[label="",style="dashed", color="red", weight=0]; 15[label="primEvenNat vx3000",fontsize=16,color="magenta"];15 -> 17[label="",style="dashed", color="magenta", weight=3]; 16[label="MyFalse",fontsize=16,color="green",shape="box"];17[label="vx3000",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_primEvenNat(Main.Succ(Main.Succ(vx3000))) -> new_primEvenNat(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_primEvenNat(Main.Succ(Main.Succ(vx3000))) -> new_primEvenNat(vx3000) The graph contains the following edges 1 > 1 ---------------------------------------- (8) YES