/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) LR [EQUIVALENT, 0 ms] (2) HASKELL (3) IPR [EQUIVALENT, 0 ms] (4) HASKELL (5) BR [EQUIVALENT, 0 ms] (6) HASKELL (7) COR [EQUIVALENT, 0 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) QDP (11) QDPSizeChangeProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (1) LR (EQUIVALENT) Lambda Reductions: The following Lambda expression "\(a,b)~(as,bs)->(a : as,b : bs)" is transformed to "unzip0 (a,b) ~(as,bs) = (a : as,b : bs); " ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (3) IPR (EQUIVALENT) IrrPat Reductions: The variables of the following irrefutable Pattern "~(as,bs)" are replaced by calls to these functions "unzip00 (as,bs) = as; " "unzip01 (as,bs) = bs; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (5) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="unzip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="unzip vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="foldr unzip0 ([],[]) vy3",fontsize=16,color="burlywood",shape="triangle"];20[label="vy3/vy30 : vy31",fontsize=10,color="white",style="solid",shape="box"];4 -> 20[label="",style="solid", color="burlywood", weight=9]; 20 -> 5[label="",style="solid", color="burlywood", weight=3]; 21[label="vy3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 21[label="",style="solid", color="burlywood", weight=9]; 21 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="foldr unzip0 ([],[]) (vy30 : vy31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="foldr unzip0 ([],[]) []",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="unzip0 vy30 (foldr unzip0 ([],[]) vy31)",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 8[label="([],[])",fontsize=16,color="green",shape="box"];10 -> 4[label="",style="dashed", color="red", weight=0]; 10[label="foldr unzip0 ([],[]) vy31",fontsize=16,color="magenta"];10 -> 11[label="",style="dashed", color="magenta", weight=3]; 9[label="unzip0 vy30 vy4",fontsize=16,color="burlywood",shape="triangle"];22[label="vy30/(vy300,vy301)",fontsize=10,color="white",style="solid",shape="box"];9 -> 22[label="",style="solid", color="burlywood", weight=9]; 22 -> 12[label="",style="solid", color="burlywood", weight=3]; 11[label="vy31",fontsize=16,color="green",shape="box"];12[label="unzip0 (vy300,vy301) vy4",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 13[label="(vy300 : unzip00 vy4,vy301 : unzip01 vy4)",fontsize=16,color="green",shape="box"];13 -> 14[label="",style="dashed", color="green", weight=3]; 13 -> 15[label="",style="dashed", color="green", weight=3]; 14[label="unzip00 vy4",fontsize=16,color="burlywood",shape="box"];23[label="vy4/(vy40,vy41)",fontsize=10,color="white",style="solid",shape="box"];14 -> 23[label="",style="solid", color="burlywood", weight=9]; 23 -> 16[label="",style="solid", color="burlywood", weight=3]; 15[label="unzip01 vy4",fontsize=16,color="burlywood",shape="box"];24[label="vy4/(vy40,vy41)",fontsize=10,color="white",style="solid",shape="box"];15 -> 24[label="",style="solid", color="burlywood", weight=9]; 24 -> 17[label="",style="solid", color="burlywood", weight=3]; 16[label="unzip00 (vy40,vy41)",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3]; 17[label="unzip01 (vy40,vy41)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3]; 18[label="vy40",fontsize=16,color="green",shape="box"];19[label="vy41",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldr(:(vy30, vy31), h, ba) -> new_foldr(vy31, h, ba) 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_foldr(:(vy30, vy31), h, ba) -> new_foldr(vy31, h, ba) The graph contains the following edges 1 > 1, 2 >= 2, 3 >= 3 ---------------------------------------- (12) YES