/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could be proven: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4)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) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) 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 "max x y|x <= yy|otherwisex; " is transformed to "max x y = max2 x y; " "max1 x y True = y; max1 x y False = max0 x y otherwise; " "max0 x y True = x; " "max2 x y = max1 x y (x <= y); " 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="maximum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="maximum vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="foldl1 max vx3",fontsize=16,color="burlywood",shape="box"];33[label="vx3/vx30 : vx31",fontsize=10,color="white",style="solid",shape="box"];4 -> 33[label="",style="solid", color="burlywood", weight=9]; 33 -> 5[label="",style="solid", color="burlywood", weight=3]; 34[label="vx3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 34[label="",style="solid", color="burlywood", weight=9]; 34 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="foldl1 max (vx30 : vx31)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="foldl1 max []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7[label="foldl max vx30 vx31",fontsize=16,color="burlywood",shape="triangle"];35[label="vx31/vx310 : vx311",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9]; 35 -> 9[label="",style="solid", color="burlywood", weight=3]; 36[label="vx31/[]",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9]; 36 -> 10[label="",style="solid", color="burlywood", weight=3]; 8[label="error []",fontsize=16,color="red",shape="box"];9[label="foldl max vx30 (vx310 : vx311)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3]; 10[label="foldl max vx30 []",fontsize=16,color="black",shape="box"];10 -> 12[label="",style="solid", color="black", weight=3]; 11 -> 7[label="",style="dashed", color="red", weight=0]; 11[label="foldl max (max vx30 vx310) vx311",fontsize=16,color="magenta"];11 -> 13[label="",style="dashed", color="magenta", weight=3]; 11 -> 14[label="",style="dashed", color="magenta", weight=3]; 12[label="vx30",fontsize=16,color="green",shape="box"];13[label="vx311",fontsize=16,color="green",shape="box"];14[label="max vx30 vx310",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3]; 15[label="max2 vx30 vx310",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3]; 16[label="max1 vx30 vx310 (vx30 <= vx310)",fontsize=16,color="burlywood",shape="box"];37[label="vx30/False",fontsize=10,color="white",style="solid",shape="box"];16 -> 37[label="",style="solid", color="burlywood", weight=9]; 37 -> 17[label="",style="solid", color="burlywood", weight=3]; 38[label="vx30/True",fontsize=10,color="white",style="solid",shape="box"];16 -> 38[label="",style="solid", color="burlywood", weight=9]; 38 -> 18[label="",style="solid", color="burlywood", weight=3]; 17[label="max1 False vx310 (False <= vx310)",fontsize=16,color="burlywood",shape="box"];39[label="vx310/False",fontsize=10,color="white",style="solid",shape="box"];17 -> 39[label="",style="solid", color="burlywood", weight=9]; 39 -> 19[label="",style="solid", color="burlywood", weight=3]; 40[label="vx310/True",fontsize=10,color="white",style="solid",shape="box"];17 -> 40[label="",style="solid", color="burlywood", weight=9]; 40 -> 20[label="",style="solid", color="burlywood", weight=3]; 18[label="max1 True vx310 (True <= vx310)",fontsize=16,color="burlywood",shape="box"];41[label="vx310/False",fontsize=10,color="white",style="solid",shape="box"];18 -> 41[label="",style="solid", color="burlywood", weight=9]; 41 -> 21[label="",style="solid", color="burlywood", weight=3]; 42[label="vx310/True",fontsize=10,color="white",style="solid",shape="box"];18 -> 42[label="",style="solid", color="burlywood", weight=9]; 42 -> 22[label="",style="solid", color="burlywood", weight=3]; 19[label="max1 False False (False <= False)",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3]; 20[label="max1 False True (False <= True)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3]; 21[label="max1 True False (True <= False)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3]; 22[label="max1 True True (True <= True)",fontsize=16,color="black",shape="box"];22 -> 26[label="",style="solid", color="black", weight=3]; 23[label="max1 False False True",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 24[label="max1 False True True",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 25[label="max1 True False False",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 26[label="max1 True True True",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="False",fontsize=16,color="green",shape="box"];28[label="True",fontsize=16,color="green",shape="box"];29[label="max0 True False otherwise",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3]; 30[label="True",fontsize=16,color="green",shape="box"];31[label="max0 True False True",fontsize=16,color="black",shape="box"];31 -> 32[label="",style="solid", color="black", weight=3]; 32[label="True",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_foldl(vx30, :(vx310, vx311)) -> new_foldl(new_max1(vx30, vx310), vx311) The TRS R consists of the following rules: new_max1(True, True) -> True new_max1(False, False) -> False new_max1(False, True) -> True new_max1(True, False) -> True The set Q consists of the following terms: new_max1(False, False) new_max1(True, True) new_max1(False, True) new_max1(True, False) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) 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_foldl(vx30, :(vx310, vx311)) -> new_foldl(new_max1(vx30, vx310), vx311) The graph contains the following edges 2 > 2 ---------------------------------------- (8) YES