/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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="sequence_",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="sequence_ vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="foldr (>>) (return ()) vy3",fontsize=16,color="burlywood",shape="triangle"];25[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 25[label="",style="solid", color="burlywood", weight=9]; 25 -> 5[label="",style="solid", color="burlywood", weight=3]; 26[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 26[label="",style="solid", color="burlywood", weight=9]; 26 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="foldr (>>) (return ()) (vy30 : vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="foldr (>>) (return ()) []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7 -> 9[label="",style="dashed", color="red", weight=0]; 7[label="(>>) vy30 foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 8[label="return ()",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3]; 10 -> 4[label="",style="dashed", color="red", weight=0]; 10[label="foldr (>>) (return ()) vy31",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3]; 9[label="(>>) vy30 vy4",fontsize=16,color="black",shape="triangle"];9 -> 13[label="",style="solid", color="black", weight=3]; 11[label="primretIO ()",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3]; 12[label="vy31",fontsize=16,color="green",shape="box"];13[label="vy30 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3]; 14[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];15[label="primbindIO vy30 (gtGt0 vy4)",fontsize=16,color="burlywood",shape="box"];27[label="vy30/IO vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 27[label="",style="solid", color="burlywood", weight=9]; 27 -> 16[label="",style="solid", color="burlywood", weight=3]; 28[label="vy30/AProVE_IO vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 28[label="",style="solid", color="burlywood", weight=9]; 28 -> 17[label="",style="solid", color="burlywood", weight=3]; 29[label="vy30/AProVE_Exception vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 29[label="",style="solid", color="burlywood", weight=9]; 29 -> 18[label="",style="solid", color="burlywood", weight=3]; 30[label="vy30/AProVE_Error vy300",fontsize=10,color="white",style="solid",shape="box"];15 -> 30[label="",style="solid", color="burlywood", weight=9]; 30 -> 19[label="",style="solid", color="burlywood", weight=3]; 16[label="primbindIO (IO vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 17[label="primbindIO (AProVE_IO vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3]; 18[label="primbindIO (AProVE_Exception vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3]; 19[label="primbindIO (AProVE_Error vy300) (gtGt0 vy4)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="error []",fontsize=16,color="red",shape="box"];21[label="gtGt0 vy4 vy300",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3]; 22[label="AProVE_Exception vy300",fontsize=16,color="green",shape="box"];23[label="AProVE_Error vy300",fontsize=16,color="green",shape="box"];24[label="vy4",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(:(vy30, vy31), h) -> new_foldr(vy31, h) 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(:(vy30, vy31), h) -> new_foldr(vy31, h) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (10) YES