/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) CR [EQUIVALENT, 0 ms] (4) HASKELL (5) IFR [EQUIVALENT, 0 ms] (6) HASKELL (7) BR [EQUIVALENT, 0 ms] (8) HASKELL (9) COR [EQUIVALENT, 0 ms] (10) HASKELL (11) Narrow [SOUND, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\vu39->case vu39 of { x -> if p x then x : [] else []; _ -> []} " is transformed to "filter0 p vu39 = case vu39 of { x -> if p x then x : [] else []; _ -> []} ; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) CR (EQUIVALENT) Case Reductions: The following Case expression "case vu39 of { x -> if p x then x : [] else []; _ -> []} " is transformed to "filter00 p x = if p x then x : [] else []; filter00 p _ = []; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) IFR (EQUIVALENT) If Reductions: The following If expression "if p x then x : [] else []" is transformed to "filter000 x True = x : []; filter000 x False = []; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (10) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (11) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="filter",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="filter vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="filter vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="concatMap (filter0 vy3) vy4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="concat . map (filter0 vy3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="concat (map (filter0 vy3) vy4)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 8[label="foldr (++) [] (map (filter0 vy3) vy4)",fontsize=16,color="burlywood",shape="triangle"];31[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];8 -> 31[label="",style="solid", color="burlywood", weight=9]; 31 -> 9[label="",style="solid", color="burlywood", weight=3]; 32[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];8 -> 32[label="",style="solid", color="burlywood", weight=9]; 32 -> 10[label="",style="solid", color="burlywood", weight=3]; 9[label="foldr (++) [] (map (filter0 vy3) (vy40 : vy41))",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="foldr (++) [] (map (filter0 vy3) [])",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="foldr (++) [] (filter0 vy3 vy40 : map (filter0 vy3) vy41)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12[label="foldr (++) [] []",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3]; 13 -> 15[label="",style="dashed", color="red", weight=0]; 13[label="(++) filter0 vy3 vy40 foldr (++) [] (map (filter0 vy3) vy41)",fontsize=16,color="magenta"];13 -> 16[label="",style="dashed", color="magenta", weight=3]; 14[label="[]",fontsize=16,color="green",shape="box"];16 -> 8[label="",style="dashed", color="red", weight=0]; 16[label="foldr (++) [] (map (filter0 vy3) vy41)",fontsize=16,color="magenta"];16 -> 17[label="",style="dashed", color="magenta", weight=3]; 15[label="(++) filter0 vy3 vy40 vy5",fontsize=16,color="black",shape="triangle"];15 -> 18[label="",style="solid", color="black", weight=3]; 17[label="vy41",fontsize=16,color="green",shape="box"];18[label="(++) filter00 vy3 vy40 vy5",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 19 -> 20[label="",style="dashed", color="red", weight=0]; 19[label="(++) filter000 vy40 (vy3 vy40) vy5",fontsize=16,color="magenta"];19 -> 21[label="",style="dashed", color="magenta", weight=3]; 21[label="vy3 vy40",fontsize=16,color="green",shape="box"];21 -> 25[label="",style="dashed", color="green", weight=3]; 20[label="(++) filter000 vy40 vy6 vy5",fontsize=16,color="burlywood",shape="triangle"];33[label="vy6/False",fontsize=10,color="white",style="solid",shape="box"];20 -> 33[label="",style="solid", color="burlywood", weight=9]; 33 -> 23[label="",style="solid", color="burlywood", weight=3]; 34[label="vy6/True",fontsize=10,color="white",style="solid",shape="box"];20 -> 34[label="",style="solid", color="burlywood", weight=9]; 34 -> 24[label="",style="solid", color="burlywood", weight=3]; 25[label="vy40",fontsize=16,color="green",shape="box"];23[label="(++) filter000 vy40 False vy5",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3]; 24[label="(++) filter000 vy40 True vy5",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3]; 26[label="(++) [] vy5",fontsize=16,color="black",shape="triangle"];26 -> 28[label="",style="solid", color="black", weight=3]; 27[label="(++) (vy40 : []) vy5",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3]; 28[label="vy5",fontsize=16,color="green",shape="box"];29[label="vy40 : [] ++ vy5",fontsize=16,color="green",shape="box"];29 -> 30[label="",style="dashed", color="green", weight=3]; 30 -> 26[label="",style="dashed", color="red", weight=0]; 30[label="[] ++ vy5",fontsize=16,color="magenta"];} ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(vy3, :(vy40, vy41), h) -> new_foldr(vy3, vy41, 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_foldr(vy3, :(vy40, vy41), h) -> new_foldr(vy3, vy41, h) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3 ---------------------------------------- (14) YES