/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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 Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; isPrefixOf :: Eq a => [a] -> [a] -> Bool; isPrefixOf [] _ = True; isPrefixOf _ [] = False; isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; isPrefixOf :: Eq a => [a] -> [a] -> Bool; isPrefixOf [] vy = True; isPrefixOf vz [] = False; isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; } module Main where { import qualified List; import qualified Maybe; 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 Maybe where { import qualified List; import qualified Main; import qualified Prelude; } module List where { import qualified Main; import qualified Maybe; import qualified Prelude; isPrefixOf :: Eq a => [a] -> [a] -> Bool; isPrefixOf [] vy = True; isPrefixOf vz [] = False; isPrefixOf (x : xs) (y : ys) = x == y && isPrefixOf xs ys; } module Main where { import qualified List; import qualified Maybe; import qualified Prelude; } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="List.isPrefixOf",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="List.isPrefixOf wu3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="List.isPrefixOf wu3 wu4",fontsize=16,color="burlywood",shape="triangle"];20[label="wu3/wu30 : wu31",fontsize=10,color="white",style="solid",shape="box"];4 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 5[label="",style="solid", color="burlywood", weight=3]; 21[label="wu3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="List.isPrefixOf (wu30 : wu31) wu4",fontsize=16,color="burlywood",shape="box"];22[label="wu4/wu40 : wu41",fontsize=10,color="white",style="solid",shape="box"];5 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 7[label="",style="solid", color="burlywood", weight=3]; 23[label="wu4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 8[label="",style="solid", color="burlywood", weight=3]; 6[label="List.isPrefixOf [] wu4",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3]; 7[label="List.isPrefixOf (wu30 : wu31) (wu40 : wu41)",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3]; 8[label="List.isPrefixOf (wu30 : wu31) []",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 9[label="True",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="red", weight=0]; 10[label="wu30 == wu40 && List.isPrefixOf wu31 wu41",fontsize=16,color="magenta"];10 -> 13[label="",style="dashed", color="magenta", weight=3]; 11[label="False",fontsize=16,color="green",shape="box"];13 -> 4[label="",style="dashed", color="red", weight=0]; 13[label="List.isPrefixOf wu31 wu41",fontsize=16,color="magenta"];13 -> 14[label="",style="dashed", color="magenta", weight=3]; 13 -> 15[label="",style="dashed", color="magenta", weight=3]; 12[label="wu30 == wu40 && wu5",fontsize=16,color="burlywood",shape="triangle"];24[label="wu30/()",fontsize=10,color="white",style="solid",shape="box"];12 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 16[label="",style="solid", color="burlywood", weight=3]; 14[label="wu41",fontsize=16,color="green",shape="box"];15[label="wu31",fontsize=16,color="green",shape="box"];16[label="() == wu40 && wu5",fontsize=16,color="burlywood",shape="box"];25[label="wu40/()",fontsize=10,color="white",style="solid",shape="box"];16 -> 25[label="",style="solid", color="burlywood", weight=9]; 25 -> 17[label="",style="solid", color="burlywood", weight=3]; 17[label="() == () && wu5",fontsize=16,color="black",shape="box"];17 -> 18[label="",style="solid", color="black", weight=3]; 18[label="True && wu5",fontsize=16,color="black",shape="box"];18 -> 19[label="",style="solid", color="black", weight=3]; 19[label="wu5",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_isPrefixOf(:(wu30, wu31), :(wu40, wu41)) -> new_isPrefixOf(wu31, wu41) 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_isPrefixOf(:(wu30, wu31), :(wu40, wu41)) -> new_isPrefixOf(wu31, wu41) The graph contains the following edges 1 > 1, 2 > 2 ---------------------------------------- (8) YES