8.03/3.52 YES 9.43/3.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.43/3.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.43/3.95 9.43/3.95 9.43/3.95 H-Termination with start terms of the given HASKELL could be proven: 9.43/3.95 9.43/3.95 (0) HASKELL 9.43/3.95 (1) BR [EQUIVALENT, 0 ms] 9.43/3.95 (2) HASKELL 9.43/3.95 (3) COR [EQUIVALENT, 0 ms] 9.43/3.95 (4) HASKELL 9.43/3.95 (5) Narrow [EQUIVALENT, 6 ms] 9.43/3.95 (6) YES 9.43/3.95 9.43/3.95 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (0) 9.43/3.95 Obligation: 9.43/3.95 mainModule Main 9.43/3.95 module Main where { 9.43/3.95 import qualified Prelude; 9.43/3.95 } 9.43/3.95 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (1) BR (EQUIVALENT) 9.43/3.95 Replaced joker patterns by fresh variables and removed binding patterns. 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (2) 9.43/3.95 Obligation: 9.43/3.95 mainModule Main 9.43/3.95 module Main where { 9.43/3.95 import qualified Prelude; 9.43/3.95 } 9.43/3.95 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (3) COR (EQUIVALENT) 9.43/3.95 Cond Reductions: 9.43/3.95 The following Function with conditions 9.43/3.95 "max x y|x <= yy|otherwisex; 9.43/3.95 " 9.43/3.95 is transformed to 9.43/3.95 "max x y = max2 x y; 9.43/3.95 " 9.43/3.95 "max0 x y True = x; 9.43/3.95 " 9.43/3.95 "max1 x y True = y; 9.43/3.95 max1 x y False = max0 x y otherwise; 9.43/3.95 " 9.43/3.95 "max2 x y = max1 x y (x <= y); 9.43/3.95 " 9.43/3.95 The following Function with conditions 9.43/3.95 "undefined |Falseundefined; 9.43/3.95 " 9.43/3.95 is transformed to 9.43/3.95 "undefined = undefined1; 9.43/3.95 " 9.43/3.95 "undefined0 True = undefined; 9.43/3.95 " 9.43/3.95 "undefined1 = undefined0 False; 9.43/3.95 " 9.43/3.95 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (4) 9.43/3.95 Obligation: 9.43/3.95 mainModule Main 9.43/3.95 module Main where { 9.43/3.95 import qualified Prelude; 9.43/3.95 } 9.43/3.95 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (5) Narrow (EQUIVALENT) 9.43/3.95 Haskell To QDPs 9.43/3.95 9.43/3.95 digraph dp_graph { 9.43/3.95 node [outthreshold=100, inthreshold=100];1[label="max",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.43/3.95 3[label="max vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.43/3.95 4[label="max vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.43/3.95 5[label="max2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.43/3.95 6[label="max1 vx3 vx4 (vx3 <= vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 9.43/3.95 7[label="max1 vx3 vx4 (compare vx3 vx4 /= GT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3]; 9.43/3.95 8[label="max1 vx3 vx4 (not (compare vx3 vx4 == GT))",fontsize=16,color="burlywood",shape="box"];15[label="vx3/()",fontsize=10,color="white",style="solid",shape="box"];8 -> 15[label="",style="solid", color="burlywood", weight=9]; 9.43/3.95 15 -> 9[label="",style="solid", color="burlywood", weight=3]; 9.43/3.95 9[label="max1 () vx4 (not (compare () vx4 == GT))",fontsize=16,color="burlywood",shape="box"];16[label="vx4/()",fontsize=10,color="white",style="solid",shape="box"];9 -> 16[label="",style="solid", color="burlywood", weight=9]; 9.43/3.95 16 -> 10[label="",style="solid", color="burlywood", weight=3]; 9.43/3.95 10[label="max1 () () (not (compare () () == GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3]; 9.43/3.95 11[label="max1 () () (not (EQ == GT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3]; 9.43/3.95 12[label="max1 () () (not False)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3]; 9.43/3.95 13[label="max1 () () True",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3]; 9.43/3.95 14[label="()",fontsize=16,color="green",shape="box"];} 9.43/3.95 9.43/3.95 ---------------------------------------- 9.43/3.95 9.43/3.95 (6) 9.43/3.95 YES 9.52/4.01 EOF