8.12/3.55 YES 9.45/3.98 proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs 9.45/3.98 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.45/3.98 9.45/3.98 9.45/3.98 H-Termination with start terms of the given HASKELL could be proven: 9.45/3.98 9.45/3.98 (0) HASKELL 9.45/3.98 (1) BR [EQUIVALENT, 0 ms] 9.45/3.98 (2) HASKELL 9.45/3.98 (3) COR [EQUIVALENT, 0 ms] 9.45/3.98 (4) HASKELL 9.45/3.98 (5) Narrow [EQUIVALENT, 15 ms] 9.45/3.98 (6) YES 9.45/3.98 9.45/3.98 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (0) 9.45/3.98 Obligation: 9.45/3.98 mainModule Main 9.45/3.98 module Main where { 9.45/3.98 import qualified Prelude; 9.45/3.98 } 9.45/3.98 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (1) BR (EQUIVALENT) 9.45/3.98 Replaced joker patterns by fresh variables and removed binding patterns. 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (2) 9.45/3.98 Obligation: 9.45/3.98 mainModule Main 9.45/3.98 module Main where { 9.45/3.98 import qualified Prelude; 9.45/3.98 } 9.45/3.98 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (3) COR (EQUIVALENT) 9.45/3.98 Cond Reductions: 9.45/3.98 The following Function with conditions 9.45/3.98 "max x y|x <= yy|otherwisex; 9.45/3.98 " 9.45/3.98 is transformed to 9.45/3.98 "max x y = max2 x y; 9.45/3.98 " 9.45/3.98 "max0 x y True = x; 9.45/3.98 " 9.45/3.98 "max1 x y True = y; 9.45/3.98 max1 x y False = max0 x y otherwise; 9.45/3.98 " 9.45/3.98 "max2 x y = max1 x y (x <= y); 9.45/3.98 " 9.45/3.98 The following Function with conditions 9.45/3.98 "undefined |Falseundefined; 9.45/3.98 " 9.45/3.98 is transformed to 9.45/3.98 "undefined = undefined1; 9.45/3.98 " 9.45/3.98 "undefined0 True = undefined; 9.45/3.98 " 9.45/3.98 "undefined1 = undefined0 False; 9.45/3.98 " 9.45/3.98 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (4) 9.45/3.98 Obligation: 9.45/3.98 mainModule Main 9.45/3.98 module Main where { 9.45/3.98 import qualified Prelude; 9.45/3.98 } 9.45/3.98 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (5) Narrow (EQUIVALENT) 9.45/3.98 Haskell To QDPs 9.45/3.98 9.45/3.98 digraph dp_graph { 9.45/3.98 node [outthreshold=100, inthreshold=100];1[label="max",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.45/3.98 3[label="max vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.45/3.98 4[label="max vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.45/3.98 5[label="max2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.45/3.98 6[label="max1 vx3 vx4 (vx3 <= vx4)",fontsize=16,color="burlywood",shape="box"];23[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];6 -> 23[label="",style="solid", color="burlywood", weight=9]; 9.45/3.98 23 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.45/3.98 24[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];6 -> 24[label="",style="solid", color="burlywood", weight=9]; 9.45/3.98 24 -> 8[label="",style="solid", color="burlywood", weight=3]; 9.45/3.98 7[label="max1 False vx4 (False <= vx4)",fontsize=16,color="burlywood",shape="box"];25[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 25[label="",style="solid", color="burlywood", weight=9]; 9.45/3.98 25 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.45/3.98 26[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 26[label="",style="solid", color="burlywood", weight=9]; 9.45/3.98 26 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.45/3.98 8[label="max1 True vx4 (True <= vx4)",fontsize=16,color="burlywood",shape="box"];27[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];8 -> 27[label="",style="solid", color="burlywood", weight=9]; 9.45/3.98 27 -> 11[label="",style="solid", color="burlywood", weight=3]; 9.45/3.98 28[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];8 -> 28[label="",style="solid", color="burlywood", weight=9]; 9.45/3.98 28 -> 12[label="",style="solid", color="burlywood", weight=3]; 9.45/3.98 9[label="max1 False False (False <= False)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3]; 9.45/3.98 10[label="max1 False True (False <= True)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3]; 9.45/3.98 11[label="max1 True False (True <= False)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3]; 9.45/3.98 12[label="max1 True True (True <= True)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3]; 9.45/3.98 13[label="max1 False False True",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3]; 9.45/3.98 14[label="max1 False True True",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3]; 9.45/3.98 15[label="max1 True False False",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3]; 9.45/3.98 16[label="max1 True True True",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3]; 9.45/3.98 17[label="False",fontsize=16,color="green",shape="box"];18[label="True",fontsize=16,color="green",shape="box"];19[label="max0 True False otherwise",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 9.45/3.98 20[label="True",fontsize=16,color="green",shape="box"];21[label="max0 True False True",fontsize=16,color="black",shape="box"];21 -> 22[label="",style="solid", color="black", weight=3]; 9.45/3.98 22[label="True",fontsize=16,color="green",shape="box"];} 9.45/3.98 9.45/3.98 ---------------------------------------- 9.45/3.98 9.45/3.98 (6) 9.45/3.98 YES 9.73/4.03 EOF