7.70/3.44 YES 9.05/3.89 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.05/3.89 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.05/3.89 9.05/3.89 9.05/3.89 H-Termination with start terms of the given HASKELL could be proven: 9.05/3.89 9.05/3.89 (0) HASKELL 9.05/3.89 (1) BR [EQUIVALENT, 0 ms] 9.05/3.89 (2) HASKELL 9.05/3.89 (3) COR [EQUIVALENT, 0 ms] 9.05/3.89 (4) HASKELL 9.05/3.89 (5) Narrow [EQUIVALENT, 0 ms] 9.05/3.89 (6) YES 9.05/3.89 9.05/3.89 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (0) 9.05/3.89 Obligation: 9.05/3.89 mainModule Main 9.05/3.89 module Main where { 9.05/3.89 import qualified Prelude; 9.05/3.89 data MyBool = MyTrue | MyFalse ; 9.05/3.89 9.05/3.89 data Tup0 = Tup0 ; 9.05/3.89 9.05/3.89 esEsTup0 :: Tup0 -> Tup0 -> MyBool; 9.05/3.89 esEsTup0 Tup0 Tup0 = MyTrue; 9.05/3.89 9.05/3.89 fsEsTup0 :: Tup0 -> Tup0 -> MyBool; 9.05/3.89 fsEsTup0 x y = not (esEsTup0 x y); 9.05/3.89 9.05/3.89 not :: MyBool -> MyBool; 9.05/3.89 not MyTrue = MyFalse; 9.05/3.89 not MyFalse = MyTrue; 9.05/3.89 9.05/3.89 } 9.05/3.89 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (1) BR (EQUIVALENT) 9.05/3.89 Replaced joker patterns by fresh variables and removed binding patterns. 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (2) 9.05/3.89 Obligation: 9.05/3.89 mainModule Main 9.05/3.89 module Main where { 9.05/3.89 import qualified Prelude; 9.05/3.89 data MyBool = MyTrue | MyFalse ; 9.05/3.89 9.05/3.89 data Tup0 = Tup0 ; 9.05/3.89 9.05/3.89 esEsTup0 :: Tup0 -> Tup0 -> MyBool; 9.05/3.89 esEsTup0 Tup0 Tup0 = MyTrue; 9.05/3.89 9.05/3.89 fsEsTup0 :: Tup0 -> Tup0 -> MyBool; 9.05/3.89 fsEsTup0 x y = not (esEsTup0 x y); 9.05/3.89 9.05/3.89 not :: MyBool -> MyBool; 9.05/3.89 not MyTrue = MyFalse; 9.05/3.89 not MyFalse = MyTrue; 9.05/3.89 9.05/3.89 } 9.05/3.89 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (3) COR (EQUIVALENT) 9.05/3.89 Cond Reductions: 9.05/3.89 The following Function with conditions 9.05/3.89 "undefined |Falseundefined; 9.05/3.89 " 9.05/3.89 is transformed to 9.05/3.89 "undefined = undefined1; 9.05/3.89 " 9.05/3.89 "undefined0 True = undefined; 9.05/3.89 " 9.05/3.89 "undefined1 = undefined0 False; 9.05/3.89 " 9.05/3.89 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (4) 9.05/3.89 Obligation: 9.05/3.89 mainModule Main 9.05/3.89 module Main where { 9.05/3.89 import qualified Prelude; 9.05/3.89 data MyBool = MyTrue | MyFalse ; 9.05/3.89 9.05/3.89 data Tup0 = Tup0 ; 9.05/3.89 9.05/3.89 esEsTup0 :: Tup0 -> Tup0 -> MyBool; 9.05/3.89 esEsTup0 Tup0 Tup0 = MyTrue; 9.05/3.89 9.05/3.89 fsEsTup0 :: Tup0 -> Tup0 -> MyBool; 9.05/3.89 fsEsTup0 x y = not (esEsTup0 x y); 9.05/3.89 9.05/3.89 not :: MyBool -> MyBool; 9.05/3.89 not MyTrue = MyFalse; 9.05/3.89 not MyFalse = MyTrue; 9.05/3.89 9.05/3.89 } 9.05/3.89 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (5) Narrow (EQUIVALENT) 9.05/3.89 Haskell To QDPs 9.05/3.89 9.05/3.89 digraph dp_graph { 9.05/3.89 node [outthreshold=100, inthreshold=100];1[label="fsEsTup0",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.05/3.89 3[label="fsEsTup0 vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.05/3.89 4[label="fsEsTup0 vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.05/3.89 5[label="not (esEsTup0 vx3 vx4)",fontsize=16,color="burlywood",shape="box"];10[label="vx3/Tup0",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9]; 9.05/3.89 10 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.05/3.89 6[label="not (esEsTup0 Tup0 vx4)",fontsize=16,color="burlywood",shape="box"];11[label="vx4/Tup0",fontsize=10,color="white",style="solid",shape="box"];6 -> 11[label="",style="solid", color="burlywood", weight=9]; 9.05/3.89 11 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.05/3.89 7[label="not (esEsTup0 Tup0 Tup0)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 9.05/3.89 8[label="not MyTrue",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9.05/3.89 9[label="MyFalse",fontsize=16,color="green",shape="box"];} 9.05/3.89 9.05/3.89 ---------------------------------------- 9.05/3.89 9.05/3.89 (6) 9.05/3.89 YES 9.27/3.93 EOF