/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) NumRed [SOUND, 0 ms] (6) HASKELL (7) Narrow [SOUND, 0 ms] (8) AND (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) 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) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="unlines",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="unlines vx3",fontsize=16,color="burlywood",shape="triangle"];24[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 4[label="",style="solid", color="burlywood", weight=3]; 25[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];3 -> 25[label="",style="solid", color="burlywood", weight=9]; 25 -> 5[label="",style="solid", color="burlywood", weight=3]; 4[label="unlines (vx30 : vx31)",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3]; 5[label="unlines []",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6 -> 12[label="",style="dashed", color="red", weight=0]; 6[label="vx30 ++ Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) : unlines vx31",fontsize=16,color="magenta"];6 -> 13[label="",style="dashed", color="magenta", weight=3]; 6 -> 14[label="",style="dashed", color="magenta", weight=3]; 6 -> 15[label="",style="dashed", color="magenta", weight=3]; 7[label="[]",fontsize=16,color="green",shape="box"];13[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];14 -> 3[label="",style="dashed", color="red", weight=0]; 14[label="unlines vx31",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3]; 15[label="vx30",fontsize=16,color="green",shape="box"];12[label="vx5 ++ Char (Succ vx6) : vx8",fontsize=16,color="burlywood",shape="triangle"];26[label="vx5/vx50 : vx51",fontsize=10,color="white",style="solid",shape="box"];12 -> 26[label="",style="solid", color="burlywood", weight=9]; 26 -> 18[label="",style="solid", color="burlywood", weight=3]; 27[label="vx5/[]",fontsize=10,color="white",style="solid",shape="box"];12 -> 27[label="",style="solid", color="burlywood", weight=9]; 27 -> 19[label="",style="solid", color="burlywood", weight=3]; 17[label="vx31",fontsize=16,color="green",shape="box"];18[label="(vx50 : vx51) ++ Char (Succ vx6) : vx8",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="[] ++ Char (Succ vx6) : vx8",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="vx50 : vx51 ++ Char (Succ vx6) : vx8",fontsize=16,color="green",shape="box"];20 -> 22[label="",style="dashed", color="green", weight=3]; 21[label="Char (Succ vx6) : vx8",fontsize=16,color="green",shape="box"];22 -> 12[label="",style="dashed", color="red", weight=0]; 22[label="vx51 ++ Char (Succ vx6) : vx8",fontsize=16,color="magenta"];22 -> 23[label="",style="dashed", color="magenta", weight=3]; 23[label="vx51",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_unlines(:(vx30, vx31)) -> new_unlines(vx31) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (10) 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_unlines(:(vx30, vx31)) -> new_unlines(vx31) The graph contains the following edges 1 > 1 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(vx50, vx51), vx6, vx8) -> new_psPs(vx51, vx6, vx8) 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_psPs(:(vx50, vx51), vx6, vx8) -> new_psPs(vx51, vx6, vx8) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (14) YES