7.39/3.45 YES 8.92/3.89 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 8.92/3.89 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 8.92/3.89 8.92/3.89 8.92/3.89 H-Termination with start terms of the given HASKELL could be proven: 8.92/3.89 8.92/3.89 (0) HASKELL 8.92/3.89 (1) BR [EQUIVALENT, 0 ms] 8.92/3.89 (2) HASKELL 8.92/3.89 (3) COR [EQUIVALENT, 0 ms] 8.92/3.89 (4) HASKELL 8.92/3.89 (5) Narrow [EQUIVALENT, 0 ms] 8.92/3.89 (6) YES 8.92/3.89 8.92/3.89 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (0) 8.92/3.89 Obligation: 8.92/3.89 mainModule Main 8.92/3.89 module Main where { 8.92/3.89 import qualified Prelude; 8.92/3.89 data Float = Float MyInt MyInt ; 8.92/3.89 8.92/3.89 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.92/3.89 8.92/3.89 data Main.Nat = Succ Main.Nat | Zero ; 8.92/3.89 8.92/3.89 floatDigitsFloat :: Float -> MyInt; 8.92/3.89 floatDigitsFloat vv = primFloatDigits; 8.92/3.89 8.92/3.89 primFloatDigits :: MyInt; 8.92/3.89 primFloatDigits = Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))); 8.92/3.89 8.92/3.89 } 8.92/3.89 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (1) BR (EQUIVALENT) 8.92/3.89 Replaced joker patterns by fresh variables and removed binding patterns. 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (2) 8.92/3.89 Obligation: 8.92/3.89 mainModule Main 8.92/3.89 module Main where { 8.92/3.89 import qualified Prelude; 8.92/3.89 data Float = Float MyInt MyInt ; 8.92/3.89 8.92/3.89 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.92/3.89 8.92/3.89 data Main.Nat = Succ Main.Nat | Zero ; 8.92/3.89 8.92/3.89 floatDigitsFloat :: Float -> MyInt; 8.92/3.89 floatDigitsFloat vv = primFloatDigits; 8.92/3.89 8.92/3.89 primFloatDigits :: MyInt; 8.92/3.89 primFloatDigits = Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))); 8.92/3.89 8.92/3.89 } 8.92/3.89 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (3) COR (EQUIVALENT) 8.92/3.89 Cond Reductions: 8.92/3.89 The following Function with conditions 8.92/3.89 "undefined |Falseundefined; 8.92/3.89 " 8.92/3.89 is transformed to 8.92/3.89 "undefined = undefined1; 8.92/3.89 " 8.92/3.89 "undefined0 True = undefined; 8.92/3.89 " 8.92/3.89 "undefined1 = undefined0 False; 8.92/3.89 " 8.92/3.89 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (4) 8.92/3.89 Obligation: 8.92/3.89 mainModule Main 8.92/3.89 module Main where { 8.92/3.89 import qualified Prelude; 8.92/3.89 data Float = Float MyInt MyInt ; 8.92/3.89 8.92/3.89 data MyInt = Pos Main.Nat | Neg Main.Nat ; 8.92/3.89 8.92/3.89 data Main.Nat = Succ Main.Nat | Zero ; 8.92/3.89 8.92/3.89 floatDigitsFloat :: Float -> MyInt; 8.92/3.89 floatDigitsFloat vv = primFloatDigits; 8.92/3.89 8.92/3.89 primFloatDigits :: MyInt; 8.92/3.89 primFloatDigits = Main.Pos (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ (Main.Succ Main.Zero)))))))))))))))))))))))); 8.92/3.89 8.92/3.89 } 8.92/3.89 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (5) Narrow (EQUIVALENT) 8.92/3.89 Haskell To QDPs 8.92/3.89 8.92/3.89 digraph dp_graph { 8.92/3.89 node [outthreshold=100, inthreshold=100];1[label="floatDigitsFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 8.92/3.89 3[label="floatDigitsFloat vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 8.92/3.89 4[label="primFloatDigits",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3]; 8.92/3.89 5[label="Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];} 8.92/3.89 8.92/3.89 ---------------------------------------- 8.92/3.89 8.92/3.89 (6) 8.92/3.89 YES 9.21/3.94 EOF