7.19/3.53 YES 8.88/4.02 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 8.88/4.02 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.88/4.02 8.88/4.02 8.88/4.02 H-Termination with start terms of the given HASKELL could be proven: 8.88/4.02 8.88/4.02 (0) HASKELL 8.88/4.02 (1) BR [EQUIVALENT, 0 ms] 8.88/4.02 (2) HASKELL 8.88/4.02 (3) COR [EQUIVALENT, 0 ms] 8.88/4.02 (4) HASKELL 8.88/4.02 (5) Narrow [EQUIVALENT, 0 ms] 8.88/4.02 (6) YES 8.88/4.02 8.88/4.02 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (0) 8.88/4.02 Obligation: 8.88/4.02 mainModule Main 8.88/4.02 module Main where { 8.88/4.02 import qualified Prelude; 8.88/4.02 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.88/4.02 8.88/4.02 data Main.Nat = Succ Main.Nat | Zero ; 8.88/4.02 8.88/4.02 predMyInt :: MyInt -> MyInt; 8.88/4.02 predMyInt (Main.Pos Main.Zero) = Main.Neg (Main.Succ Main.Zero); 8.88/4.02 predMyInt (Main.Neg Main.Zero) = Main.Neg (Main.Succ Main.Zero); 8.88/4.02 predMyInt (Main.Pos (Main.Succ x)) = Main.Pos x; 8.88/4.02 predMyInt (Main.Neg (Main.Succ x)) = Main.Neg (Main.Succ (Main.Succ x)); 8.88/4.02 8.88/4.02 } 8.88/4.02 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (1) BR (EQUIVALENT) 8.88/4.02 Replaced joker patterns by fresh variables and removed binding patterns. 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (2) 8.88/4.02 Obligation: 8.88/4.02 mainModule Main 8.88/4.02 module Main where { 8.88/4.02 import qualified Prelude; 8.88/4.02 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.88/4.02 8.88/4.02 data Main.Nat = Succ Main.Nat | Zero ; 8.88/4.02 8.88/4.02 predMyInt :: MyInt -> MyInt; 8.88/4.02 predMyInt (Main.Pos Main.Zero) = Main.Neg (Main.Succ Main.Zero); 8.88/4.02 predMyInt (Main.Neg Main.Zero) = Main.Neg (Main.Succ Main.Zero); 8.88/4.02 predMyInt (Main.Pos (Main.Succ x)) = Main.Pos x; 8.88/4.02 predMyInt (Main.Neg (Main.Succ x)) = Main.Neg (Main.Succ (Main.Succ x)); 8.88/4.02 8.88/4.02 } 8.88/4.02 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (3) COR (EQUIVALENT) 8.88/4.02 Cond Reductions: 8.88/4.02 The following Function with conditions 8.88/4.02 "undefined |Falseundefined; 8.88/4.02 " 8.88/4.02 is transformed to 8.88/4.02 "undefined = undefined1; 8.88/4.02 " 8.88/4.02 "undefined0 True = undefined; 8.88/4.02 " 8.88/4.02 "undefined1 = undefined0 False; 8.88/4.02 " 8.88/4.02 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (4) 8.88/4.02 Obligation: 8.88/4.02 mainModule Main 8.88/4.02 module Main where { 8.88/4.02 import qualified Prelude; 8.88/4.02 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.88/4.02 8.88/4.02 data Main.Nat = Succ Main.Nat | Zero ; 8.88/4.02 8.88/4.02 predMyInt :: MyInt -> MyInt; 8.88/4.02 predMyInt (Main.Pos Main.Zero) = Main.Neg (Main.Succ Main.Zero); 8.88/4.02 predMyInt (Main.Neg Main.Zero) = Main.Neg (Main.Succ Main.Zero); 8.88/4.02 predMyInt (Main.Pos (Main.Succ x)) = Main.Pos x; 8.88/4.02 predMyInt (Main.Neg (Main.Succ x)) = Main.Neg (Main.Succ (Main.Succ x)); 8.88/4.02 8.88/4.02 } 8.88/4.02 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (5) Narrow (EQUIVALENT) 8.88/4.02 Haskell To QDPs 8.88/4.02 8.88/4.02 digraph dp_graph { 8.88/4.02 node [outthreshold=100, inthreshold=100];1[label="predMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 8.88/4.02 3[label="predMyInt vx3",fontsize=16,color="burlywood",shape="triangle"];14[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 14[label="",style="solid", color="burlywood", weight=9]; 8.88/4.02 14 -> 4[label="",style="solid", color="burlywood", weight=3]; 8.88/4.02 15[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];3 -> 15[label="",style="solid", color="burlywood", weight=9]; 8.88/4.02 15 -> 5[label="",style="solid", color="burlywood", weight=3]; 8.88/4.02 4[label="predMyInt (Pos vx30)",fontsize=16,color="burlywood",shape="box"];16[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9]; 8.88/4.02 16 -> 6[label="",style="solid", color="burlywood", weight=3]; 8.88/4.02 17[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9]; 8.88/4.02 17 -> 7[label="",style="solid", color="burlywood", weight=3]; 8.88/4.02 5[label="predMyInt (Neg vx30)",fontsize=16,color="burlywood",shape="box"];18[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9]; 8.88/4.02 18 -> 8[label="",style="solid", color="burlywood", weight=3]; 8.88/4.02 19[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];5 -> 19[label="",style="solid", color="burlywood", weight=9]; 8.88/4.02 19 -> 9[label="",style="solid", color="burlywood", weight=3]; 8.88/4.02 6[label="predMyInt (Pos (Succ vx300))",fontsize=16,color="black",shape="box"];6 -> 10[label="",style="solid", color="black", weight=3]; 8.88/4.02 7[label="predMyInt (Pos Zero)",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3]; 8.88/4.02 8[label="predMyInt (Neg (Succ vx300))",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3]; 8.88/4.02 9[label="predMyInt (Neg Zero)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 8.88/4.02 10[label="Pos vx300",fontsize=16,color="green",shape="box"];11[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];12[label="Neg (Succ (Succ vx300))",fontsize=16,color="green",shape="box"];13[label="Neg (Succ Zero)",fontsize=16,color="green",shape="box"];} 8.88/4.02 8.88/4.02 ---------------------------------------- 8.88/4.02 8.88/4.02 (6) 8.88/4.02 YES 9.13/4.06 EOF