/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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) Narrow [SOUND, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\_->q" is transformed to "gtGt0 q _ = q; " ---------------------------------------- (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) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="mapM_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="mapM_ vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="mapM_ vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="sequence_ . map vy3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6[label="sequence_ (map vy3 vy4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7[label="foldr (>>) (return ()) (map vy3 vy4)",fontsize=16,color="burlywood",shape="triangle"];28[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];7 -> 28[label="",style="solid", color="burlywood", weight=9]; 28 -> 8[label="",style="solid", color="burlywood", weight=3]; 29[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 29[label="",style="solid", color="burlywood", weight=9]; 29 -> 9[label="",style="solid", color="burlywood", weight=3]; 8[label="foldr (>>) (return ()) (map vy3 (vy40 : vy41))",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3]; 9[label="foldr (>>) (return ()) (map vy3 [])",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="foldr (>>) (return ()) (vy3 vy40 : map vy3 vy41)",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3]; 12 -> 14[label="",style="dashed", color="red", weight=0]; 12[label="(>>) vy3 vy40 foldr (>>) (return ()) (map vy3 vy41)",fontsize=16,color="magenta"];12 -> 15[label="",style="dashed", color="magenta", weight=3]; 13[label="return ()",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3]; 15 -> 7[label="",style="dashed", color="red", weight=0]; 15[label="foldr (>>) (return ()) (map vy3 vy41)",fontsize=16,color="magenta"];15 -> 17[label="",style="dashed", color="magenta", weight=3]; 14[label="(>>) vy3 vy40 vy5",fontsize=16,color="black",shape="triangle"];14 -> 18[label="",style="solid", color="black", weight=3]; 16[label="Just ()",fontsize=16,color="green",shape="box"];17[label="vy41",fontsize=16,color="green",shape="box"];18 -> 19[label="",style="dashed", color="red", weight=0]; 18[label="vy3 vy40 >>= gtGt0 vy5",fontsize=16,color="magenta"];18 -> 20[label="",style="dashed", color="magenta", weight=3]; 20[label="vy3 vy40",fontsize=16,color="green",shape="box"];20 -> 24[label="",style="dashed", color="green", weight=3]; 19[label="vy6 >>= gtGt0 vy5",fontsize=16,color="burlywood",shape="triangle"];30[label="vy6/Nothing",fontsize=10,color="white",style="solid",shape="box"];19 -> 30[label="",style="solid", color="burlywood", weight=9]; 30 -> 22[label="",style="solid", color="burlywood", weight=3]; 31[label="vy6/Just vy60",fontsize=10,color="white",style="solid",shape="box"];19 -> 31[label="",style="solid", color="burlywood", weight=9]; 31 -> 23[label="",style="solid", color="burlywood", weight=3]; 24[label="vy40",fontsize=16,color="green",shape="box"];22[label="Nothing >>= gtGt0 vy5",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3]; 23[label="Just vy60 >>= gtGt0 vy5",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3]; 25[label="Nothing",fontsize=16,color="green",shape="box"];26[label="gtGt0 vy5 vy60",fontsize=16,color="black",shape="box"];26 -> 27[label="",style="solid", color="black", weight=3]; 27[label="vy5",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(vy3, :(vy40, vy41), h, ba) -> new_foldr(vy3, vy41, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) 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, ba) -> new_foldr(vy3, vy41, h, ba) The graph contains the following edges 1 >= 1, 2 > 2, 3 >= 3, 4 >= 4 ---------------------------------------- (10) YES