/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) AND (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) 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) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="(>>=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(>>=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(>>=) vx3 vx4",fontsize=16,color="blue",shape="box"];43[label=">>= :: (Maybe a) -> (a -> Maybe b) -> Maybe b",fontsize=10,color="white",style="solid",shape="box"];4 -> 43[label="",style="solid", color="blue", weight=9]; 43 -> 5[label="",style="solid", color="blue", weight=3]; 44[label=">>= :: ([] a) -> (a -> [] b) -> [] b",fontsize=10,color="white",style="solid",shape="box"];4 -> 44[label="",style="solid", color="blue", weight=9]; 44 -> 6[label="",style="solid", color="blue", weight=3]; 45[label=">>= :: (IO a) -> (a -> IO b) -> IO b",fontsize=10,color="white",style="solid",shape="box"];4 -> 45[label="",style="solid", color="blue", weight=9]; 45 -> 7[label="",style="solid", color="blue", weight=3]; 5[label="(>>=) vx3 vx4",fontsize=16,color="burlywood",shape="box"];46[label="vx3/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 8[label="",style="solid", color="burlywood", weight=3]; 47[label="vx3/Just vx30",fontsize=10,color="white",style="solid",shape="box"];5 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 9[label="",style="solid", color="burlywood", weight=3]; 6[label="(>>=) vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];48[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];6 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 10[label="",style="solid", color="burlywood", weight=3]; 49[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];6 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 11[label="",style="solid", color="burlywood", weight=3]; 7[label="(>>=) vx3 vx4",fontsize=16,color="black",shape="box"];7 -> 12[label="",style="solid", color="black", weight=3]; 8[label="(>>=) Nothing vx4",fontsize=16,color="black",shape="box"];8 -> 13[label="",style="solid", color="black", weight=3]; 9[label="(>>=) Just vx30 vx4",fontsize=16,color="black",shape="box"];9 -> 14[label="",style="solid", color="black", weight=3]; 10[label="(>>=) vx30 : vx31 vx4",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3]; 11[label="(>>=) [] vx4",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3]; 12[label="primbindIO vx3 vx4",fontsize=16,color="burlywood",shape="box"];50[label="vx3/IO vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 50[label="",style="solid", color="burlywood", weight=9]; 50 -> 17[label="",style="solid", color="burlywood", weight=3]; 51[label="vx3/AProVE_IO vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 51[label="",style="solid", color="burlywood", weight=9]; 51 -> 18[label="",style="solid", color="burlywood", weight=3]; 52[label="vx3/AProVE_Exception vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 52[label="",style="solid", color="burlywood", weight=9]; 52 -> 19[label="",style="solid", color="burlywood", weight=3]; 53[label="vx3/AProVE_Error vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 53[label="",style="solid", color="burlywood", weight=9]; 53 -> 20[label="",style="solid", color="burlywood", weight=3]; 13[label="Nothing",fontsize=16,color="green",shape="box"];14[label="vx4 vx30",fontsize=16,color="green",shape="box"];14 -> 21[label="",style="dashed", color="green", weight=3]; 15 -> 29[label="",style="dashed", color="red", weight=0]; 15[label="vx4 vx30 ++ (vx31 >>= vx4)",fontsize=16,color="magenta"];15 -> 30[label="",style="dashed", color="magenta", weight=3]; 15 -> 31[label="",style="dashed", color="magenta", weight=3]; 16[label="[]",fontsize=16,color="green",shape="box"];17[label="primbindIO (IO vx30) vx4",fontsize=16,color="black",shape="box"];17 -> 24[label="",style="solid", color="black", weight=3]; 18[label="primbindIO (AProVE_IO vx30) vx4",fontsize=16,color="black",shape="box"];18 -> 25[label="",style="solid", color="black", weight=3]; 19[label="primbindIO (AProVE_Exception vx30) vx4",fontsize=16,color="black",shape="box"];19 -> 26[label="",style="solid", color="black", weight=3]; 20[label="primbindIO (AProVE_Error vx30) vx4",fontsize=16,color="black",shape="box"];20 -> 27[label="",style="solid", color="black", weight=3]; 21[label="vx30",fontsize=16,color="green",shape="box"];30 -> 6[label="",style="dashed", color="red", weight=0]; 30[label="vx31 >>= vx4",fontsize=16,color="magenta"];30 -> 33[label="",style="dashed", color="magenta", weight=3]; 31[label="vx4 vx30",fontsize=16,color="green",shape="box"];31 -> 34[label="",style="dashed", color="green", weight=3]; 29[label="vx6 ++ vx5",fontsize=16,color="burlywood",shape="triangle"];54[label="vx6/vx60 : vx61",fontsize=10,color="white",style="solid",shape="box"];29 -> 54[label="",style="solid", color="burlywood", weight=9]; 54 -> 35[label="",style="solid", color="burlywood", weight=3]; 55[label="vx6/[]",fontsize=10,color="white",style="solid",shape="box"];29 -> 55[label="",style="solid", color="burlywood", weight=9]; 55 -> 36[label="",style="solid", color="burlywood", weight=3]; 24[label="error []",fontsize=16,color="red",shape="box"];25[label="vx4 vx30",fontsize=16,color="green",shape="box"];25 -> 37[label="",style="dashed", color="green", weight=3]; 26[label="AProVE_Exception vx30",fontsize=16,color="green",shape="box"];27[label="AProVE_Error vx30",fontsize=16,color="green",shape="box"];33[label="vx31",fontsize=16,color="green",shape="box"];34[label="vx30",fontsize=16,color="green",shape="box"];35[label="(vx60 : vx61) ++ vx5",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3]; 36[label="[] ++ vx5",fontsize=16,color="black",shape="box"];36 -> 40[label="",style="solid", color="black", weight=3]; 37[label="vx30",fontsize=16,color="green",shape="box"];39[label="vx60 : vx61 ++ vx5",fontsize=16,color="green",shape="box"];39 -> 41[label="",style="dashed", color="green", weight=3]; 40[label="vx5",fontsize=16,color="green",shape="box"];41 -> 29[label="",style="dashed", color="red", weight=0]; 41[label="vx61 ++ vx5",fontsize=16,color="magenta"];41 -> 42[label="",style="dashed", color="magenta", weight=3]; 42[label="vx61",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Complex Obligation (AND) ---------------------------------------- (7) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs(:(vx30, vx31), vx4, h, ba) -> new_gtGtEs(vx31, vx4, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (8) 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_gtGtEs(:(vx30, vx31), vx4, h, ba) -> new_gtGtEs(vx31, vx4, h, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 ---------------------------------------- (9) YES ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(vx60, vx61), vx5, h) -> new_psPs(vx61, vx5, h) 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_psPs(:(vx60, vx61), vx5, h) -> new_psPs(vx61, vx5, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (12) YES