/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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) 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) 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="(>>)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="(>>) vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="(>>) vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="vy3 >>= gtGt0 vy4",fontsize=16,color="burlywood",shape="triangle"];20[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];5 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 6[label="",style="solid", color="burlywood", weight=3]; 21[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];5 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 7[label="",style="solid", color="burlywood", weight=3]; 6[label="vy30 : vy31 >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="[] >>= gtGt0 vy4",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 8 -> 10[label="",style="dashed", color="red", weight=0]; 8[label="gtGt0 vy4 vy30 ++ (vy31 >>= gtGt0 vy4)",fontsize=16,color="magenta"];8 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="[]",fontsize=16,color="green",shape="box"];11 -> 5[label="",style="dashed", color="red", weight=0]; 11[label="vy31 >>= gtGt0 vy4",fontsize=16,color="magenta"];11 -> 12[label="",style="dashed", color="magenta", weight=3]; 10[label="gtGt0 vy4 vy30 ++ vy5",fontsize=16,color="black",shape="triangle"];10 -> 13[label="",style="solid", color="black", weight=3]; 12[label="vy31",fontsize=16,color="green",shape="box"];13[label="vy4 ++ vy5",fontsize=16,color="burlywood",shape="triangle"];22[label="vy4/vy40 : vy41",fontsize=10,color="white",style="solid",shape="box"];13 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 14[label="",style="solid", color="burlywood", weight=3]; 23[label="vy4/[]",fontsize=10,color="white",style="solid",shape="box"];13 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 15[label="",style="solid", color="burlywood", weight=3]; 14[label="(vy40 : vy41) ++ vy5",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3]; 15[label="[] ++ vy5",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3]; 16[label="vy40 : vy41 ++ vy5",fontsize=16,color="green",shape="box"];16 -> 18[label="",style="dashed", color="green", weight=3]; 17[label="vy5",fontsize=16,color="green",shape="box"];18 -> 13[label="",style="dashed", color="red", weight=0]; 18[label="vy41 ++ vy5",fontsize=16,color="magenta"];18 -> 19[label="",style="dashed", color="magenta", weight=3]; 19[label="vy41",fontsize=16,color="green",shape="box"];} ---------------------------------------- (8) Complex Obligation (AND) ---------------------------------------- (9) Obligation: Q DP problem: The TRS P consists of the following rules: new_gtGtEs(:(vy30, vy31), vy4, h, ba) -> new_gtGtEs(vy31, vy4, h, ba) 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_gtGtEs(:(vy30, vy31), vy4, h, ba) -> new_gtGtEs(vy31, vy4, h, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3, 4 >= 4 ---------------------------------------- (11) YES ---------------------------------------- (12) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(vy40, vy41), vy5, h) -> new_psPs(vy41, vy5, h) 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(:(vy40, vy41), vy5, h) -> new_psPs(vy41, vy5, h) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (14) YES