/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4) HASKELL (5) COR [EQUIVALENT, 0 ms] (6) HASKELL (7) LetRed [EQUIVALENT, 0 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\(q : _)->q" is transformed to "q1 (q : _) = q; " The following Lambda expression "\qs->qs" is transformed to "qs0 qs = qs; " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "f x q : qs where { q = q1 vu40; ; q1 (q : vv) = q; ; qs = qs0 vu40; ; qs0 qs = qs; ; vu40 = scanr f q0 xs; } " are unpacked to the following functions on top level "scanrQ vy vz wu = scanrQ1 vy vz wu (scanrVu40 vy vz wu); " "scanrVu40 vy vz wu = scanr vy vz wu; " "scanrQ1 vy vz wu (q : vv) = q; " "scanrQs vy vz wu = scanrQs0 vy vz wu (scanrVu40 vy vz wu); " "scanrQs0 vy vz wu qs = qs; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="scanr",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="scanr wv3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="scanr wv3 wv4",fontsize=16,color="grey",shape="box"];4 -> 5[label="",style="dashed", color="grey", weight=3]; 5[label="scanr wv3 wv4 wv5",fontsize=16,color="burlywood",shape="triangle"];27[label="wv5/wv50 : wv51",fontsize=10,color="white",style="solid",shape="box"];5 -> 27[label="",style="solid", color="burlywood", weight=9]; 27 -> 6[label="",style="solid", color="burlywood", weight=3]; 28[label="wv5/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 28[label="",style="solid", color="burlywood", weight=9]; 28 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="scanr wv3 wv4 (wv50 : wv51)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="scanr wv3 wv4 []",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8[label="wv3 wv50 (scanrQ wv3 wv4 wv51) : scanrQs wv3 wv4 wv51",fontsize=16,color="green",shape="box"];8 -> 10[label="",style="dashed", color="green", weight=3]; 8 -> 11[label="",style="dashed", color="green", weight=3]; 9[label="wv4 : []",fontsize=16,color="green",shape="box"];10[label="wv3 wv50 (scanrQ wv3 wv4 wv51)",fontsize=16,color="green",shape="box"];10 -> 12[label="",style="dashed", color="green", weight=3]; 10 -> 13[label="",style="dashed", color="green", weight=3]; 11[label="scanrQs wv3 wv4 wv51",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 12[label="wv50",fontsize=16,color="green",shape="box"];13[label="scanrQ wv3 wv4 wv51",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="scanrQs0 wv3 wv4 wv51 (scanrVu40 wv3 wv4 wv51)",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15 -> 19[label="",style="dashed", color="red", weight=0]; 15[label="scanrQ1 wv3 wv4 wv51 (scanrVu40 wv3 wv4 wv51)",fontsize=16,color="magenta"];15 -> 20[label="",style="dashed", color="magenta", weight=3]; 16[label="scanrVu40 wv3 wv4 wv51",fontsize=16,color="black",shape="triangle"];16 -> 18[label="",style="solid", color="black", weight=3]; 20 -> 16[label="",style="dashed", color="red", weight=0]; 20[label="scanrVu40 wv3 wv4 wv51",fontsize=16,color="magenta"];19[label="scanrQ1 wv3 wv4 wv51 wv6",fontsize=16,color="burlywood",shape="triangle"];29[label="wv6/wv60 : wv61",fontsize=10,color="white",style="solid",shape="box"];19 -> 29[label="",style="solid", color="burlywood", weight=9]; 29 -> 22[label="",style="solid", color="burlywood", weight=3]; 30[label="wv6/[]",fontsize=10,color="white",style="solid",shape="box"];19 -> 30[label="",style="solid", color="burlywood", weight=9]; 30 -> 23[label="",style="solid", color="burlywood", weight=3]; 18 -> 5[label="",style="dashed", color="red", weight=0]; 18[label="scanr wv3 wv4 wv51",fontsize=16,color="magenta"];18 -> 24[label="",style="dashed", color="magenta", weight=3]; 22[label="scanrQ1 wv3 wv4 wv51 (wv60 : wv61)",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3]; 23[label="scanrQ1 wv3 wv4 wv51 []",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3]; 24[label="wv51",fontsize=16,color="green",shape="box"];25[label="wv60",fontsize=16,color="green",shape="box"];26[label="error []",fontsize=16,color="red",shape="box"];} ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_scanr(wv3, wv4, :(wv50, wv51), h, ba) -> new_scanrVu40(wv3, wv4, wv51, h, ba) new_scanrVu40(wv3, wv4, wv51, h, ba) -> new_scanr(wv3, wv4, wv51, h, ba) new_scanr(wv3, wv4, :(wv50, wv51), h, ba) -> new_scanr(wv3, wv4, wv51, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (11) 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_scanrVu40(wv3, wv4, wv51, h, ba) -> new_scanr(wv3, wv4, wv51, h, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 >= 3, 4 >= 4, 5 >= 5 *new_scanr(wv3, wv4, :(wv50, wv51), h, ba) -> new_scanr(wv3, wv4, wv51, h, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 *new_scanr(wv3, wv4, :(wv50, wv51), h, ba) -> new_scanrVu40(wv3, wv4, wv51, h, ba) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 >= 4, 5 >= 5 ---------------------------------------- (12) YES