7.86/3.54 YES 9.51/4.00 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.51/4.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.51/4.00 9.51/4.00 9.51/4.00 H-Termination with start terms of the given HASKELL could be proven: 9.51/4.00 9.51/4.00 (0) HASKELL 9.51/4.00 (1) BR [EQUIVALENT, 0 ms] 9.51/4.00 (2) HASKELL 9.51/4.00 (3) COR [EQUIVALENT, 0 ms] 9.51/4.00 (4) HASKELL 9.51/4.00 (5) Narrow [EQUIVALENT, 0 ms] 9.51/4.00 (6) YES 9.51/4.00 9.51/4.00 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (0) 9.51/4.00 Obligation: 9.51/4.00 mainModule Main 9.51/4.00 module Main where { 9.51/4.00 import qualified Prelude; 9.51/4.00 data Float = Float MyInt MyInt ; 9.51/4.00 9.51/4.00 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.51/4.00 9.51/4.00 data Main.Nat = Succ Main.Nat | Zero ; 9.51/4.00 9.51/4.00 negateFloat :: Float -> Float; 9.51/4.00 negateFloat = primNegFloat; 9.51/4.00 9.51/4.00 negateMyInt :: MyInt -> MyInt; 9.51/4.00 negateMyInt = primNegInt; 9.51/4.00 9.51/4.00 primNegFloat :: Float -> Float; 9.51/4.00 primNegFloat (Float x1 x2) = Float (negateMyInt x1) x2; 9.51/4.00 9.51/4.00 primNegInt :: MyInt -> MyInt; 9.51/4.00 primNegInt (Main.Pos x) = Main.Neg x; 9.51/4.00 primNegInt (Main.Neg x) = Main.Pos x; 9.51/4.00 9.51/4.00 } 9.51/4.00 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (1) BR (EQUIVALENT) 9.51/4.00 Replaced joker patterns by fresh variables and removed binding patterns. 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (2) 9.51/4.00 Obligation: 9.51/4.00 mainModule Main 9.51/4.00 module Main where { 9.51/4.00 import qualified Prelude; 9.51/4.00 data Float = Float MyInt MyInt ; 9.51/4.00 9.51/4.00 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.51/4.00 9.51/4.00 data Main.Nat = Succ Main.Nat | Zero ; 9.51/4.00 9.51/4.00 negateFloat :: Float -> Float; 9.51/4.00 negateFloat = primNegFloat; 9.51/4.00 9.51/4.00 negateMyInt :: MyInt -> MyInt; 9.51/4.00 negateMyInt = primNegInt; 9.51/4.00 9.51/4.00 primNegFloat :: Float -> Float; 9.51/4.00 primNegFloat (Float x1 x2) = Float (negateMyInt x1) x2; 9.51/4.00 9.51/4.00 primNegInt :: MyInt -> MyInt; 9.51/4.00 primNegInt (Main.Pos x) = Main.Neg x; 9.51/4.00 primNegInt (Main.Neg x) = Main.Pos x; 9.51/4.00 9.51/4.00 } 9.51/4.00 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (3) COR (EQUIVALENT) 9.51/4.00 Cond Reductions: 9.51/4.00 The following Function with conditions 9.51/4.00 "undefined |Falseundefined; 9.51/4.00 " 9.51/4.00 is transformed to 9.51/4.00 "undefined = undefined1; 9.51/4.00 " 9.51/4.00 "undefined0 True = undefined; 9.51/4.00 " 9.51/4.00 "undefined1 = undefined0 False; 9.51/4.00 " 9.51/4.00 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (4) 9.51/4.00 Obligation: 9.51/4.00 mainModule Main 9.51/4.00 module Main where { 9.51/4.00 import qualified Prelude; 9.51/4.00 data Float = Float MyInt MyInt ; 9.51/4.00 9.51/4.00 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.51/4.00 9.51/4.00 data Main.Nat = Succ Main.Nat | Zero ; 9.51/4.00 9.51/4.00 negateFloat :: Float -> Float; 9.51/4.00 negateFloat = primNegFloat; 9.51/4.00 9.51/4.00 negateMyInt :: MyInt -> MyInt; 9.51/4.00 negateMyInt = primNegInt; 9.51/4.00 9.51/4.00 primNegFloat :: Float -> Float; 9.51/4.00 primNegFloat (Float x1 x2) = Float (negateMyInt x1) x2; 9.51/4.00 9.51/4.00 primNegInt :: MyInt -> MyInt; 9.51/4.00 primNegInt (Main.Pos x) = Main.Neg x; 9.51/4.00 primNegInt (Main.Neg x) = Main.Pos x; 9.51/4.00 9.51/4.00 } 9.51/4.00 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (5) Narrow (EQUIVALENT) 9.51/4.00 Haskell To QDPs 9.51/4.00 9.51/4.00 digraph dp_graph { 9.51/4.00 node [outthreshold=100, inthreshold=100];1[label="negateFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.51/4.00 3[label="negateFloat vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.51/4.00 4[label="primNegFloat vx3",fontsize=16,color="burlywood",shape="box"];13[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 13[label="",style="solid", color="burlywood", weight=9]; 9.51/4.00 13 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.51/4.00 5[label="primNegFloat (Float vx30 vx31)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.51/4.00 6[label="Float (negateMyInt vx30) vx31",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3]; 9.51/4.00 7[label="negateMyInt vx30",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 9.51/4.00 8[label="primNegInt vx30",fontsize=16,color="burlywood",shape="box"];14[label="vx30/Pos vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 14[label="",style="solid", color="burlywood", weight=9]; 9.51/4.00 14 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.51/4.00 15[label="vx30/Neg vx300",fontsize=10,color="white",style="solid",shape="box"];8 -> 15[label="",style="solid", color="burlywood", weight=9]; 9.51/4.00 15 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.51/4.00 9[label="primNegInt (Pos vx300)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 9.51/4.00 10[label="primNegInt (Neg vx300)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 9.51/4.00 11[label="Neg vx300",fontsize=16,color="green",shape="box"];12[label="Pos vx300",fontsize=16,color="green",shape="box"];} 9.51/4.00 9.51/4.00 ---------------------------------------- 9.51/4.00 9.51/4.00 (6) 9.51/4.00 YES 9.51/4.05 EOF