/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.hs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) QDP (7) NonTerminationLoopProof [COMPLETE, 0 ms] (8) NO (9) Narrow [COMPLETE, 0 ms] (10) QDP (11) PisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; data MyBool = MyTrue | MyFalse ; until :: (a -> MyBool) -> (a -> a) -> a -> a; until p f x = until0 x p f (p x); until0 x p f MyTrue = x; until0 x p f MyFalse = until p f (f x); } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; data MyBool = MyTrue | MyFalse ; until :: (a -> MyBool) -> (a -> a) -> a -> a; until p f x = until0 x p f (p x); until0 x p f MyTrue = x; until0 x p f MyFalse = until p f (f x); } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; data MyBool = MyTrue | MyFalse ; until :: (a -> MyBool) -> (a -> a) -> a -> a; until p f x = until0 x p f (p x); until0 x p f MyTrue = x; until0 x p f MyFalse = until p f (f x); } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="until",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="until vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="until vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="until vx3 vx4 vx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 7[label="",style="dashed", color="red", weight=0]; 6[label="until0 vx5 vx3 vx4 (vx3 vx5)",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3]; 8[label="vx3 vx5",fontsize=16,color="green",shape="box"];8 -> 12[label="",style="dashed", color="green", weight=3]; 7[label="until0 vx5 vx3 vx4 vx6",fontsize=16,color="burlywood",shape="triangle"];17[label="vx6/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 17[label="",style="solid", color="burlywood", weight=9]; 17 -> 10[label="",style="solid", color="burlywood", weight=3]; 18[label="vx6/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 18[label="",style="solid", color="burlywood", weight=9]; 18 -> 11[label="",style="solid", color="burlywood", weight=3]; 12[label="vx5",fontsize=16,color="green",shape="box"];10[label="until0 vx5 vx3 vx4 MyTrue",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3]; 11[label="until0 vx5 vx3 vx4 MyFalse",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 13[label="vx5",fontsize=16,color="green",shape="box"];14 -> 5[label="",style="dashed", color="red", weight=0]; 14[label="until vx3 vx4 (vx4 vx5)",fontsize=16,color="magenta"];14 -> 15[label="",style="dashed", color="magenta", weight=3]; 15[label="vx4 vx5",fontsize=16,color="green",shape="box"];15 -> 16[label="",style="dashed", color="green", weight=3]; 16[label="vx5",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_until(vx3, vx4, h) -> new_until0(vx3, vx4, h) new_until0(vx3, vx4, h) -> new_until(vx3, vx4, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by narrowing to the left: s = new_until0(vx3', vx4', h') evaluates to t =new_until0(vx3', vx4', h') Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence new_until0(vx3', vx4', h') -> new_until(vx3', vx4', h') with rule new_until0(vx3'', vx4'', h'') -> new_until(vx3'', vx4'', h'') at position [] and matcher [vx3'' / vx3', vx4'' / vx4', h'' / h'] new_until(vx3', vx4', h') -> new_until0(vx3', vx4', h') with rule new_until(vx3, vx4, h) -> new_until0(vx3, vx4, h) Now applying the matcher to the start term leads to a term which is equal to the last term in the rewriting sequence All these steps are and every following step will be a correct step w.r.t to Q. ---------------------------------------- (8) NO ---------------------------------------- (9) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="until",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="until vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="until vx3 vx4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="until vx3 vx4 vx5",fontsize=16,color="black",shape="triangle"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 7[label="",style="dashed", color="red", weight=0]; 6[label="until0 vx5 vx3 vx4 (vx3 vx5)",fontsize=16,color="magenta"];6 -> 8[label="",style="dashed", color="magenta", weight=3]; 8[label="vx3 vx5",fontsize=16,color="green",shape="box"];8 -> 12[label="",style="dashed", color="green", weight=3]; 7[label="until0 vx5 vx3 vx4 vx6",fontsize=16,color="burlywood",shape="triangle"];17[label="vx6/MyTrue",fontsize=10,color="white",style="solid",shape="box"];7 -> 17[label="",style="solid", color="burlywood", weight=9]; 17 -> 10[label="",style="solid", color="burlywood", weight=3]; 18[label="vx6/MyFalse",fontsize=10,color="white",style="solid",shape="box"];7 -> 18[label="",style="solid", color="burlywood", weight=9]; 18 -> 11[label="",style="solid", color="burlywood", weight=3]; 12[label="vx5",fontsize=16,color="green",shape="box"];10[label="until0 vx5 vx3 vx4 MyTrue",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3]; 11[label="until0 vx5 vx3 vx4 MyFalse",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 13[label="vx5",fontsize=16,color="green",shape="box"];14 -> 5[label="",style="dashed", color="red", weight=0]; 14[label="until vx3 vx4 (vx4 vx5)",fontsize=16,color="magenta"];14 -> 15[label="",style="dashed", color="magenta", weight=3]; 15[label="vx4 vx5",fontsize=16,color="green",shape="box"];15 -> 16[label="",style="dashed", color="green", weight=3]; 16[label="vx5",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Obligation: Q DP problem: P is empty. R is empty. Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (11) PisEmptyProof (EQUIVALENT) The TRS P is empty. Hence, there is no (P,Q,R) chain. ---------------------------------------- (12) YES