7.48/3.51 YES 8.90/3.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 8.90/3.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.90/3.95 8.90/3.95 8.90/3.95 H-Termination with start terms of the given HASKELL could be proven: 8.90/3.95 8.90/3.95 (0) HASKELL 8.90/3.95 (1) BR [EQUIVALENT, 0 ms] 8.90/3.95 (2) HASKELL 8.90/3.95 (3) COR [EQUIVALENT, 0 ms] 8.90/3.95 (4) HASKELL 8.90/3.95 (5) Narrow [EQUIVALENT, 0 ms] 8.90/3.95 (6) YES 8.90/3.95 8.90/3.95 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (0) 8.90/3.95 Obligation: 8.90/3.95 mainModule Main 8.90/3.95 module Main where { 8.90/3.95 import qualified Prelude; 8.90/3.95 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.90/3.95 8.90/3.95 data Main.Nat = Succ Main.Nat | Zero ; 8.90/3.95 8.90/3.95 data Ordering = LT | EQ | GT ; 8.90/3.95 8.90/3.95 fromEnumOrdering :: Ordering -> MyInt; 8.90/3.95 fromEnumOrdering LT = Main.Pos Main.Zero; 8.90/3.95 fromEnumOrdering EQ = Main.Pos (Main.Succ Main.Zero); 8.90/3.95 fromEnumOrdering GT = Main.Pos (Main.Succ (Main.Succ Main.Zero)); 8.90/3.95 8.90/3.95 } 8.90/3.95 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (1) BR (EQUIVALENT) 8.90/3.95 Replaced joker patterns by fresh variables and removed binding patterns. 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (2) 8.90/3.95 Obligation: 8.90/3.95 mainModule Main 8.90/3.95 module Main where { 8.90/3.95 import qualified Prelude; 8.90/3.95 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.90/3.95 8.90/3.95 data Main.Nat = Succ Main.Nat | Zero ; 8.90/3.95 8.90/3.95 data Ordering = LT | EQ | GT ; 8.90/3.95 8.90/3.95 fromEnumOrdering :: Ordering -> MyInt; 8.90/3.95 fromEnumOrdering LT = Main.Pos Main.Zero; 8.90/3.95 fromEnumOrdering EQ = Main.Pos (Main.Succ Main.Zero); 8.90/3.95 fromEnumOrdering GT = Main.Pos (Main.Succ (Main.Succ Main.Zero)); 8.90/3.95 8.90/3.95 } 8.90/3.95 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (3) COR (EQUIVALENT) 8.90/3.95 Cond Reductions: 8.90/3.95 The following Function with conditions 8.90/3.95 "undefined |Falseundefined; 8.90/3.95 " 8.90/3.95 is transformed to 8.90/3.95 "undefined = undefined1; 8.90/3.95 " 8.90/3.95 "undefined0 True = undefined; 8.90/3.95 " 8.90/3.95 "undefined1 = undefined0 False; 8.90/3.95 " 8.90/3.95 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (4) 8.90/3.95 Obligation: 8.90/3.95 mainModule Main 8.90/3.95 module Main where { 8.90/3.95 import qualified Prelude; 8.90/3.95 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.90/3.95 8.90/3.95 data Main.Nat = Succ Main.Nat | Zero ; 8.90/3.95 8.90/3.95 data Ordering = LT | EQ | GT ; 8.90/3.95 8.90/3.95 fromEnumOrdering :: Ordering -> MyInt; 8.90/3.95 fromEnumOrdering LT = Main.Pos Main.Zero; 8.90/3.95 fromEnumOrdering EQ = Main.Pos (Main.Succ Main.Zero); 8.90/3.95 fromEnumOrdering GT = Main.Pos (Main.Succ (Main.Succ Main.Zero)); 8.90/3.95 8.90/3.95 } 8.90/3.95 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (5) Narrow (EQUIVALENT) 8.90/3.95 Haskell To QDPs 8.90/3.95 8.90/3.95 digraph dp_graph { 8.90/3.95 node [outthreshold=100, inthreshold=100];1[label="fromEnumOrdering",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 8.90/3.95 3[label="fromEnumOrdering vx3",fontsize=16,color="burlywood",shape="triangle"];10[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];3 -> 10[label="",style="solid", color="burlywood", weight=9]; 8.90/3.95 10 -> 4[label="",style="solid", color="burlywood", weight=3]; 8.90/3.95 11[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];3 -> 11[label="",style="solid", color="burlywood", weight=9]; 8.90/3.95 11 -> 5[label="",style="solid", color="burlywood", weight=3]; 8.90/3.95 12[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];3 -> 12[label="",style="solid", color="burlywood", weight=9]; 8.90/3.95 12 -> 6[label="",style="solid", color="burlywood", weight=3]; 8.90/3.95 4[label="fromEnumOrdering LT",fontsize=16,color="black",shape="box"];4 -> 7[label="",style="solid", color="black", weight=3]; 8.90/3.95 5[label="fromEnumOrdering EQ",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3]; 8.90/3.95 6[label="fromEnumOrdering GT",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3]; 8.90/3.95 7[label="Pos Zero",fontsize=16,color="green",shape="box"];8[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];9[label="Pos (Succ (Succ Zero))",fontsize=16,color="green",shape="box"];} 8.90/3.95 8.90/3.95 ---------------------------------------- 8.90/3.95 8.90/3.95 (6) 8.90/3.95 YES 9.21/4.02 EOF