/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.hs /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (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) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="notElem",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="notElem vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="notElem vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="all . (/=)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="all ((/=) vx3) vx4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="and . map ((/=) vx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="and (map ((/=) vx3) vx4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9[label="foldr (&&) True (map ((/=) vx3) vx4)",fontsize=16,color="burlywood",shape="triangle"];45[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];9 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 10[label="",style="solid", color="burlywood", weight=3]; 46[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 11[label="",style="solid", color="burlywood", weight=3]; 10[label="foldr (&&) True (map ((/=) vx3) (vx40 : vx41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="foldr (&&) True (map ((/=) vx3) [])",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="foldr (&&) True (((/=) vx3 vx40) : map ((/=) vx3) vx41)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="foldr (&&) True []",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14 -> 16[label="",style="dashed", color="red", weight=0]; 14[label="(&&) (/=) vx3 vx40 foldr (&&) True (map ((/=) vx3) vx41)",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3]; 15[label="True",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0]; 17[label="foldr (&&) True (map ((/=) vx3) vx41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3]; 16[label="(&&) (/=) vx3 vx40 vx5",fontsize=16,color="black",shape="triangle"];16 -> 19[label="",style="solid", color="black", weight=3]; 18[label="vx41",fontsize=16,color="green",shape="box"];19[label="(&&) not (vx3 == vx40) vx5",fontsize=16,color="burlywood",shape="box"];47[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];19 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 20[label="",style="solid", color="burlywood", weight=3]; 48[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];19 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 21[label="",style="solid", color="burlywood", weight=3]; 49[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];19 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 22[label="",style="solid", color="burlywood", weight=3]; 20[label="(&&) not (LT == vx40) vx5",fontsize=16,color="burlywood",shape="box"];50[label="vx40/LT",fontsize=10,color="white",style="solid",shape="box"];20 -> 50[label="",style="solid", color="burlywood", weight=9]; 50 -> 23[label="",style="solid", color="burlywood", weight=3]; 51[label="vx40/EQ",fontsize=10,color="white",style="solid",shape="box"];20 -> 51[label="",style="solid", color="burlywood", weight=9]; 51 -> 24[label="",style="solid", color="burlywood", weight=3]; 52[label="vx40/GT",fontsize=10,color="white",style="solid",shape="box"];20 -> 52[label="",style="solid", color="burlywood", weight=9]; 52 -> 25[label="",style="solid", color="burlywood", weight=3]; 21[label="(&&) not (EQ == vx40) vx5",fontsize=16,color="burlywood",shape="box"];53[label="vx40/LT",fontsize=10,color="white",style="solid",shape="box"];21 -> 53[label="",style="solid", color="burlywood", weight=9]; 53 -> 26[label="",style="solid", color="burlywood", weight=3]; 54[label="vx40/EQ",fontsize=10,color="white",style="solid",shape="box"];21 -> 54[label="",style="solid", color="burlywood", weight=9]; 54 -> 27[label="",style="solid", color="burlywood", weight=3]; 55[label="vx40/GT",fontsize=10,color="white",style="solid",shape="box"];21 -> 55[label="",style="solid", color="burlywood", weight=9]; 55 -> 28[label="",style="solid", color="burlywood", weight=3]; 22[label="(&&) not (GT == vx40) vx5",fontsize=16,color="burlywood",shape="box"];56[label="vx40/LT",fontsize=10,color="white",style="solid",shape="box"];22 -> 56[label="",style="solid", color="burlywood", weight=9]; 56 -> 29[label="",style="solid", color="burlywood", weight=3]; 57[label="vx40/EQ",fontsize=10,color="white",style="solid",shape="box"];22 -> 57[label="",style="solid", color="burlywood", weight=9]; 57 -> 30[label="",style="solid", color="burlywood", weight=3]; 58[label="vx40/GT",fontsize=10,color="white",style="solid",shape="box"];22 -> 58[label="",style="solid", color="burlywood", weight=9]; 58 -> 31[label="",style="solid", color="burlywood", weight=3]; 23[label="(&&) not (LT == LT) vx5",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3]; 24[label="(&&) not (LT == EQ) vx5",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3]; 25[label="(&&) not (LT == GT) vx5",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3]; 26[label="(&&) not (EQ == LT) vx5",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3]; 27[label="(&&) not (EQ == EQ) vx5",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3]; 28[label="(&&) not (EQ == GT) vx5",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3]; 29[label="(&&) not (GT == LT) vx5",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3]; 30[label="(&&) not (GT == EQ) vx5",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3]; 31[label="(&&) not (GT == GT) vx5",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3]; 32[label="(&&) not True vx5",fontsize=16,color="black",shape="triangle"];32 -> 41[label="",style="solid", color="black", weight=3]; 33[label="(&&) not False vx5",fontsize=16,color="black",shape="triangle"];33 -> 42[label="",style="solid", color="black", weight=3]; 34 -> 33[label="",style="dashed", color="red", weight=0]; 34[label="(&&) not False vx5",fontsize=16,color="magenta"];35 -> 33[label="",style="dashed", color="red", weight=0]; 35[label="(&&) not False vx5",fontsize=16,color="magenta"];36 -> 32[label="",style="dashed", color="red", weight=0]; 36[label="(&&) not True vx5",fontsize=16,color="magenta"];37 -> 33[label="",style="dashed", color="red", weight=0]; 37[label="(&&) not False vx5",fontsize=16,color="magenta"];38 -> 33[label="",style="dashed", color="red", weight=0]; 38[label="(&&) not False vx5",fontsize=16,color="magenta"];39 -> 33[label="",style="dashed", color="red", weight=0]; 39[label="(&&) not False vx5",fontsize=16,color="magenta"];40 -> 32[label="",style="dashed", color="red", weight=0]; 40[label="(&&) not True vx5",fontsize=16,color="magenta"];41[label="(&&) False vx5",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3]; 42[label="(&&) True vx5",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3]; 43[label="False",fontsize=16,color="green",shape="box"];44[label="vx5",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(vx3, :(vx40, vx41)) -> new_foldr(vx3, vx41) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) 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_foldr(vx3, :(vx40, vx41)) -> new_foldr(vx3, vx41) The graph contains the following edges 1 >= 1, 2 > 2 ---------------------------------------- (8) YES