7.64/3.53 YES 9.23/3.99 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.23/3.99 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.23/3.99 9.23/3.99 9.23/3.99 H-Termination with start terms of the given HASKELL could be proven: 9.23/3.99 9.23/3.99 (0) HASKELL 9.23/3.99 (1) BR [EQUIVALENT, 0 ms] 9.23/3.99 (2) HASKELL 9.23/3.99 (3) COR [EQUIVALENT, 0 ms] 9.23/3.99 (4) HASKELL 9.23/3.99 (5) Narrow [EQUIVALENT, 0 ms] 9.23/3.99 (6) YES 9.23/3.99 9.23/3.99 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (0) 9.23/3.99 Obligation: 9.23/3.99 mainModule Main 9.23/3.99 module Main where { 9.23/3.99 import qualified Prelude; 9.23/3.99 data Integer = Integer MyInt ; 9.23/3.99 9.23/3.99 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.23/3.99 9.23/3.99 data Main.Nat = Succ Main.Nat | Zero ; 9.23/3.99 9.23/3.99 data Ratio a = CnPc a a ; 9.23/3.99 9.23/3.99 fromIntMyInt :: MyInt -> MyInt; 9.23/3.99 fromIntMyInt x = x; 9.23/3.99 9.23/3.99 fromIntegerMyInt :: Integer -> MyInt; 9.23/3.99 fromIntegerMyInt (Integer x) = x; 9.23/3.99 9.23/3.99 fromIntegerRatio :: Integer -> Ratio MyInt; 9.23/3.99 fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 9.23/3.99 9.23/3.99 } 9.23/3.99 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (1) BR (EQUIVALENT) 9.23/3.99 Replaced joker patterns by fresh variables and removed binding patterns. 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (2) 9.23/3.99 Obligation: 9.23/3.99 mainModule Main 9.23/3.99 module Main where { 9.23/3.99 import qualified Prelude; 9.23/3.99 data Integer = Integer MyInt ; 9.23/3.99 9.23/3.99 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.23/3.99 9.23/3.99 data Main.Nat = Succ Main.Nat | Zero ; 9.23/3.99 9.23/3.99 data Ratio a = CnPc a a ; 9.23/3.99 9.23/3.99 fromIntMyInt :: MyInt -> MyInt; 9.23/3.99 fromIntMyInt x = x; 9.23/3.99 9.23/3.99 fromIntegerMyInt :: Integer -> MyInt; 9.23/3.99 fromIntegerMyInt (Integer x) = x; 9.23/3.99 9.23/3.99 fromIntegerRatio :: Integer -> Ratio MyInt; 9.23/3.99 fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 9.23/3.99 9.23/3.99 } 9.23/3.99 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (3) COR (EQUIVALENT) 9.23/3.99 Cond Reductions: 9.23/3.99 The following Function with conditions 9.23/3.99 "undefined |Falseundefined; 9.23/3.99 " 9.23/3.99 is transformed to 9.23/3.99 "undefined = undefined1; 9.23/3.99 " 9.23/3.99 "undefined0 True = undefined; 9.23/3.99 " 9.23/3.99 "undefined1 = undefined0 False; 9.23/3.99 " 9.23/3.99 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (4) 9.23/3.99 Obligation: 9.23/3.99 mainModule Main 9.23/3.99 module Main where { 9.23/3.99 import qualified Prelude; 9.23/3.99 data Integer = Integer MyInt ; 9.23/3.99 9.23/3.99 data MyInt = Pos Main.Nat | Neg Main.Nat ; 9.23/3.99 9.23/3.99 data Main.Nat = Succ Main.Nat | Zero ; 9.23/3.99 9.23/3.99 data Ratio a = CnPc a a ; 9.23/3.99 9.23/3.99 fromIntMyInt :: MyInt -> MyInt; 9.23/3.99 fromIntMyInt x = x; 9.23/3.99 9.23/3.99 fromIntegerMyInt :: Integer -> MyInt; 9.23/3.99 fromIntegerMyInt (Integer x) = x; 9.23/3.99 9.23/3.99 fromIntegerRatio :: Integer -> Ratio MyInt; 9.23/3.99 fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))); 9.23/3.99 9.23/3.99 } 9.23/3.99 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (5) Narrow (EQUIVALENT) 9.23/3.99 Haskell To QDPs 9.23/3.99 9.23/3.99 digraph dp_graph { 9.23/3.99 node [outthreshold=100, inthreshold=100];1[label="fromIntegerRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.23/3.99 3[label="fromIntegerRatio vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 9.23/3.99 4[label="CnPc (fromIntegerMyInt vx3) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];4 -> 5[label="",style="dashed", color="green", weight=3]; 9.23/3.99 4 -> 6[label="",style="dashed", color="green", weight=3]; 9.23/3.99 5[label="fromIntegerMyInt vx3",fontsize=16,color="burlywood",shape="box"];10[label="vx3/Integer vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9]; 9.23/3.99 10 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.23/3.99 6[label="fromIntMyInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.23/3.99 7[label="fromIntegerMyInt (Integer vx30)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 9.23/3.99 8[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];9[label="vx30",fontsize=16,color="green",shape="box"];} 9.23/3.99 9.23/3.99 ---------------------------------------- 9.23/3.99 9.23/3.99 (6) 9.23/3.99 YES 9.23/4.04 EOF