/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) LetRed [EQUIVALENT, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) NonTerminationLoopProof [COMPLETE, 0 ms] (11) NO (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) Narrow [COMPLETE, 0 ms] (16) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (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; } ---------------------------------------- (5) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "xs' where { xs' = xs ++ xs'; } " are unpacked to the following functions on top level "cycleXs' vx = vx ++ cycleXs' vx; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) 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"];20[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 4[label="",style="solid", color="burlywood", weight=3]; 21[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 5[label="",style="solid", color="burlywood", weight=3]; 4[label="cycle (vy30 : vy31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 5[label="cycle []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="cycleXs' (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="(vy30 : vy31) ++ cycleXs' (vy30 : vy31)",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="error []",fontsize=16,color="red",shape="box"];11 -> 6[label="",style="dashed", color="red", weight=0]; 11[label="cycleXs' (vy30 : vy31)",fontsize=16,color="magenta"];10[label="(vy30 : vy31) ++ vy4",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3]; 12[label="vy30 : vy31 ++ vy4",fontsize=16,color="green",shape="box"];12 -> 13[label="",style="dashed", color="green", weight=3]; 13[label="vy31 ++ vy4",fontsize=16,color="burlywood",shape="triangle"];22[label="vy31/vy310 : vy311",fontsize=10,color="white",style="solid",shape="box"];13 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 14[label="",style="solid", color="burlywood", weight=3]; 23[label="vy31/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="(vy310 : vy311) ++ vy4",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="[] ++ vy4",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="vy310 : vy311 ++ vy4",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3]; 17[label="vy4",fontsize=16,color="green",shape="box"];18 -> 13[label="",style="dashed", color="red", weight=0]; 18[label="vy311 ++ vy4",fontsize=16,color="magenta"];18 -> 19[label="",style="dashed", color="magenta", weight=3]; 19[label="vy311",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) 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. ---------------------------------------- (10) 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). ---------------------------------------- (11) NO ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(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. ---------------------------------------- (13) 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(:(vy310, vy311), vy4, h) -> new_psPs(vy311, vy4, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (14) YES ---------------------------------------- (15) 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"];20[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 4[label="",style="solid", color="burlywood", weight=3]; 21[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 5[label="",style="solid", color="burlywood", weight=3]; 4[label="cycle (vy30 : vy31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 5[label="cycle []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="cycleXs' (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="(vy30 : vy31) ++ cycleXs' (vy30 : vy31)",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="error []",fontsize=16,color="red",shape="box"];11 -> 6[label="",style="dashed", color="red", weight=0]; 11[label="cycleXs' (vy30 : vy31)",fontsize=16,color="magenta"];10[label="(vy30 : vy31) ++ vy4",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3]; 12[label="vy30 : vy31 ++ vy4",fontsize=16,color="green",shape="box"];12 -> 13[label="",style="dashed", color="green", weight=3]; 13[label="vy31 ++ vy4",fontsize=16,color="burlywood",shape="triangle"];22[label="vy31/vy310 : vy311",fontsize=10,color="white",style="solid",shape="box"];13 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 14[label="",style="solid", color="burlywood", weight=3]; 23[label="vy31/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="(vy310 : vy311) ++ vy4",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="[] ++ vy4",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="vy310 : vy311 ++ vy4",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3]; 17[label="vy4",fontsize=16,color="green",shape="box"];18 -> 13[label="",style="dashed", color="red", weight=0]; 18[label="vy311 ++ vy4",fontsize=16,color="magenta"];18 -> 19[label="",style="dashed", color="magenta", weight=3]; 19[label="vy311",fontsize=16,color="green",shape="box"];} ---------------------------------------- (16) TRUE