/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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="elem",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="elem vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="elem vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="any . (==)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="any ((==) vx3) vx4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="or . map ((==) vx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="or (map ((==) vx3) vx4)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3]; 9[label="foldr (||) False (map ((==) vx3) vx4)",fontsize=16,color="burlywood",shape="triangle"];42[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];9 -> 42[label="",style="solid", color="burlywood", weight=9]; 42 -> 10[label="",style="solid", color="burlywood", weight=3]; 43[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];9 -> 43[label="",style="solid", color="burlywood", weight=9]; 43 -> 11[label="",style="solid", color="burlywood", weight=3]; 10[label="foldr (||) False (map ((==) vx3) (vx40 : vx41))",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="foldr (||) False (map ((==) vx3) [])",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="foldr (||) False (((==) vx3 vx40) : map ((==) vx3) vx41)",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13[label="foldr (||) False []",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 (||) False (map ((==) vx3) vx41)",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3]; 15[label="False",fontsize=16,color="green",shape="box"];17 -> 9[label="",style="dashed", color="red", weight=0]; 17[label="foldr (||) False (map ((==) vx3) vx41)",fontsize=16,color="magenta"];17 -> 18[label="",style="dashed", color="magenta", weight=3]; 16[label="(||) (==) vx3 vx40 vx5",fontsize=16,color="burlywood",shape="triangle"];44[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];16 -> 44[label="",style="solid", color="burlywood", weight=9]; 44 -> 19[label="",style="solid", color="burlywood", weight=3]; 45[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];16 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 20[label="",style="solid", color="burlywood", weight=3]; 46[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];16 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 21[label="",style="solid", color="burlywood", weight=3]; 18[label="vx41",fontsize=16,color="green",shape="box"];19[label="(||) (==) LT vx40 vx5",fontsize=16,color="burlywood",shape="box"];47[label="vx40/LT",fontsize=10,color="white",style="solid",shape="box"];19 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 22[label="",style="solid", color="burlywood", weight=3]; 48[label="vx40/EQ",fontsize=10,color="white",style="solid",shape="box"];19 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 23[label="",style="solid", color="burlywood", weight=3]; 49[label="vx40/GT",fontsize=10,color="white",style="solid",shape="box"];19 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 24[label="",style="solid", color="burlywood", weight=3]; 20[label="(||) (==) EQ 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 -> 25[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 -> 26[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 -> 27[label="",style="solid", color="burlywood", weight=3]; 21[label="(||) (==) GT 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 -> 28[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 -> 29[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 -> 30[label="",style="solid", color="burlywood", weight=3]; 22[label="(||) (==) LT LT vx5",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3]; 23[label="(||) (==) LT EQ vx5",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3]; 24[label="(||) (==) LT GT vx5",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3]; 25[label="(||) (==) EQ LT vx5",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3]; 26[label="(||) (==) EQ EQ vx5",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3]; 27[label="(||) (==) EQ GT vx5",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3]; 28[label="(||) (==) GT LT vx5",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3]; 29[label="(||) (==) GT EQ vx5",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3]; 30[label="(||) (==) GT GT vx5",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3]; 31[label="(||) True vx5",fontsize=16,color="black",shape="triangle"];31 -> 40[label="",style="solid", color="black", weight=3]; 32[label="(||) False vx5",fontsize=16,color="black",shape="triangle"];32 -> 41[label="",style="solid", color="black", weight=3]; 33 -> 32[label="",style="dashed", color="red", weight=0]; 33[label="(||) False vx5",fontsize=16,color="magenta"];34 -> 32[label="",style="dashed", color="red", weight=0]; 34[label="(||) False vx5",fontsize=16,color="magenta"];35 -> 31[label="",style="dashed", color="red", weight=0]; 35[label="(||) True vx5",fontsize=16,color="magenta"];36 -> 32[label="",style="dashed", color="red", weight=0]; 36[label="(||) False vx5",fontsize=16,color="magenta"];37 -> 32[label="",style="dashed", color="red", weight=0]; 37[label="(||) False vx5",fontsize=16,color="magenta"];38 -> 32[label="",style="dashed", color="red", weight=0]; 38[label="(||) False vx5",fontsize=16,color="magenta"];39 -> 31[label="",style="dashed", color="red", weight=0]; 39[label="(||) True vx5",fontsize=16,color="magenta"];40[label="True",fontsize=16,color="green",shape="box"];41[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