/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="vx4 >>= vx3",fontsize=16,color="burlywood",shape="triangle"];26[label="vx4/vx40 : vx41",fontsize=10,color="white",style="solid",shape="box"];5 -> 26[label="",style="solid", color="burlywood", weight=9]; 26 -> 6[label="",style="solid", color="burlywood", weight=3]; 27[label="vx4/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 27[label="",style="solid", color="burlywood", weight=9]; 27 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="vx40 : vx41 >>= vx3",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="[] >>= vx3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8 -> 13[label="",style="dashed", color="red", weight=0]; 8[label="vx3 vx40 ++ (vx41 >>= vx3)",fontsize=16,color="magenta"];8 -> 14[label="",style="dashed", color="magenta", weight=3]; 8 -> 15[label="",style="dashed", color="magenta", weight=3]; 9[label="[]",fontsize=16,color="green",shape="box"];14 -> 5[label="",style="dashed", color="red", weight=0]; 14[label="vx41 >>= vx3",fontsize=16,color="magenta"];14 -> 17[label="",style="dashed", color="magenta", weight=3]; 15[label="vx3 vx40",fontsize=16,color="green",shape="box"];15 -> 18[label="",style="dashed", color="green", weight=3]; 13[label="vx6 ++ vx5",fontsize=16,color="burlywood",shape="triangle"];28[label="vx6/vx60 : vx61",fontsize=10,color="white",style="solid",shape="box"];13 -> 28[label="",style="solid", color="burlywood", weight=9]; 28 -> 19[label="",style="solid", color="burlywood", weight=3]; 29[label="vx6/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 29[label="",style="solid", color="burlywood", weight=9]; 29 -> 20[label="",style="solid", color="burlywood", weight=3]; 17[label="vx41",fontsize=16,color="green",shape="box"];18[label="vx40",fontsize=16,color="green",shape="box"];19[label="(vx60 : vx61) ++ vx5",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3]; 20[label="[] ++ vx5",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3]; 22[label="vx60 : vx61 ++ vx5",fontsize=16,color="green",shape="box"];22 -> 24[label="",style="dashed", color="green", weight=3]; 23[label="vx5",fontsize=16,color="green",shape="box"];24 -> 13[label="",style="dashed", color="red", weight=0]; 24[label="vx61 ++ vx5",fontsize=16,color="magenta"];24 -> 25[label="",style="dashed", color="magenta", weight=3]; 25[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(:(vx40, vx41), vx3, h, ba) -> new_gtGtEs(vx41, vx3, 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(:(vx40, vx41), vx3, h, ba) -> new_gtGtEs(vx41, vx3, 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