/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) AND (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) NonTerminationLoopProof [COMPLETE, 0 ms] (12) NO (13) Narrow [COMPLETE, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data MyBool = MyTrue | MyFalse ; cycle :: List a -> List a; cycle Nil = Main.error; cycle xs = cycleXs' xs; cycleXs' vv = psPs vv (cycleXs' vv); error :: a; error = stop MyTrue; psPs :: List a -> List a -> List a; psPs Nil ys = ys; psPs (Cons x xs) ys = Cons x (psPs xs ys); stop :: MyBool -> a; stop MyFalse = stop MyFalse; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data MyBool = MyTrue | MyFalse ; cycle :: List a -> List a; cycle Nil = Main.error; cycle xs = cycleXs' xs; cycleXs' vv = psPs vv (cycleXs' vv); error :: a; error = stop MyTrue; psPs :: List a -> List a -> List a; psPs Nil ys = ys; psPs (Cons x xs) ys = Cons x (psPs xs ys); stop :: MyBool -> a; stop MyFalse = stop MyFalse; } ---------------------------------------- (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 List a = Cons a (List a) | Nil ; data MyBool = MyTrue | MyFalse ; cycle :: List a -> List a; cycle Nil = Main.error; cycle xs = cycleXs' xs; cycleXs' vv = psPs vv (cycleXs' vv); error :: a; error = stop MyTrue; psPs :: List a -> List a -> List a; psPs Nil ys = ys; psPs (Cons x xs) ys = Cons x (psPs xs ys); stop :: MyBool -> a; stop MyFalse = stop MyFalse; } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="cycle",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="cycle vy3",fontsize=16,color="burlywood",shape="triangle"];21[label="vy3/Cons vy30 vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 4[label="",style="solid", color="burlywood", weight=3]; 22[label="vy3/Nil",fontsize=10,color="white",style="solid",shape="box"];3 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 5[label="",style="solid", color="burlywood", weight=3]; 4[label="cycle (Cons vy30 vy31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 5[label="cycle Nil",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="cycleXs' (Cons vy30 vy31)",fontsize=16,color="black",shape="triangle"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="error",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8 -> 10[label="",style="dashed", color="red", weight=0]; 8[label="psPs (Cons vy30 vy31) (cycleXs' (Cons vy30 vy31))",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="stop MyTrue",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3]; 11 -> 6[label="",style="dashed", color="red", weight=0]; 11[label="cycleXs' (Cons vy30 vy31)",fontsize=16,color="magenta"];10[label="psPs (Cons vy30 vy31) vy4",fontsize=16,color="black",shape="triangle"];10 -> 13[label="",style="solid", color="black", weight=3]; 12[label="error []",fontsize=16,color="red",shape="box"];13[label="Cons vy30 (psPs vy31 vy4)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3]; 14[label="psPs vy31 vy4",fontsize=16,color="burlywood",shape="triangle"];23[label="vy31/Cons vy310 vy311",fontsize=10,color="white",style="solid",shape="box"];14 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 15[label="",style="solid", color="burlywood", weight=3]; 24[label="vy31/Nil",fontsize=10,color="white",style="solid",shape="box"];14 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 16[label="",style="solid", color="burlywood", weight=3]; 15[label="psPs (Cons vy310 vy311) vy4",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="psPs Nil vy4",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="Cons vy310 (psPs vy311 vy4)",fontsize=16,color="green",shape="box"];17 -> 19[label="",style="dashed", color="green", weight=3]; 18[label="vy4",fontsize=16,color="green",shape="box"];19 -> 14[label="",style="dashed", color="red", weight=0]; 19[label="psPs vy311 vy4",fontsize=16,color="magenta"];19 -> 20[label="",style="dashed", color="magenta", weight=3]; 20[label="vy311",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(Cons(vy310, vy311), vy4, h) -> new_psPs(vy311, vy4, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (8) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *new_psPs(Cons(vy310, vy311), vy4, h) -> new_psPs(vy311, vy4, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (9) YES ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_cycleXs'(vy30, vy31, h) -> new_cycleXs'(vy30, vy31, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (11) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_cycleXs'(vy30, vy31, h) evaluates to t =new_cycleXs'(vy30, vy31, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_cycleXs'(vy30, vy31, h) to new_cycleXs'(vy30, vy31, h). ---------------------------------------- (12) NO ---------------------------------------- (13) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="cycle",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="cycle vy3",fontsize=16,color="burlywood",shape="triangle"];21[label="vy3/Cons vy30 vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 4[label="",style="solid", color="burlywood", weight=3]; 22[label="vy3/Nil",fontsize=10,color="white",style="solid",shape="box"];3 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 5[label="",style="solid", color="burlywood", weight=3]; 4[label="cycle (Cons vy30 vy31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 5[label="cycle Nil",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="cycleXs' (Cons vy30 vy31)",fontsize=16,color="black",shape="triangle"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="error",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8 -> 10[label="",style="dashed", color="red", weight=0]; 8[label="psPs (Cons vy30 vy31) (cycleXs' (Cons vy30 vy31))",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="stop MyTrue",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3]; 11 -> 6[label="",style="dashed", color="red", weight=0]; 11[label="cycleXs' (Cons vy30 vy31)",fontsize=16,color="magenta"];10[label="psPs (Cons vy30 vy31) vy4",fontsize=16,color="black",shape="triangle"];10 -> 13[label="",style="solid", color="black", weight=3]; 12[label="error []",fontsize=16,color="red",shape="box"];13[label="Cons vy30 (psPs vy31 vy4)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3]; 14[label="psPs vy31 vy4",fontsize=16,color="burlywood",shape="triangle"];23[label="vy31/Cons vy310 vy311",fontsize=10,color="white",style="solid",shape="box"];14 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 15[label="",style="solid", color="burlywood", weight=3]; 24[label="vy31/Nil",fontsize=10,color="white",style="solid",shape="box"];14 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 16[label="",style="solid", color="burlywood", weight=3]; 15[label="psPs (Cons vy310 vy311) vy4",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="psPs Nil vy4",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="Cons vy310 (psPs vy311 vy4)",fontsize=16,color="green",shape="box"];17 -> 19[label="",style="dashed", color="green", weight=3]; 18[label="vy4",fontsize=16,color="green",shape="box"];19 -> 14[label="",style="dashed", color="red", weight=0]; 19[label="psPs vy311 vy4",fontsize=16,color="magenta"];19 -> 20[label="",style="dashed", color="magenta", weight=3]; 20[label="vy311",fontsize=16,color="green",shape="box"];} ---------------------------------------- (14) TRUE