7.44/3.54 YES 9.16/4.00 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.16/4.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.16/4.00 9.16/4.00 9.16/4.00 H-Termination with start terms of the given HASKELL could be proven: 9.16/4.00 9.16/4.00 (0) HASKELL 9.16/4.00 (1) BR [EQUIVALENT, 0 ms] 9.16/4.00 (2) HASKELL 9.16/4.00 (3) COR [EQUIVALENT, 0 ms] 9.16/4.00 (4) HASKELL 9.16/4.00 (5) Narrow [EQUIVALENT, 0 ms] 9.16/4.00 (6) YES 9.16/4.00 9.16/4.00 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (0) 9.16/4.00 Obligation: 9.16/4.00 mainModule Main 9.16/4.00 module Main where { 9.16/4.00 import qualified Prelude; 9.16/4.00 data Main.Maybe a = Nothing | Just a ; 9.16/4.00 9.16/4.00 esLtLt :: (a -> Main.Maybe b) -> Main.Maybe a -> Main.Maybe b; 9.16/4.00 esLtLt f x = gtGtEsMaybe x f; 9.16/4.00 9.16/4.00 gtGtEsMaybe :: Main.Maybe a -> (a -> Main.Maybe b) -> Main.Maybe b; 9.16/4.00 gtGtEsMaybe (Main.Just x) k = k x; 9.16/4.00 gtGtEsMaybe Main.Nothing k = Main.Nothing; 9.16/4.00 9.16/4.00 } 9.16/4.00 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (1) BR (EQUIVALENT) 9.16/4.00 Replaced joker patterns by fresh variables and removed binding patterns. 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (2) 9.16/4.00 Obligation: 9.16/4.00 mainModule Main 9.16/4.00 module Main where { 9.16/4.00 import qualified Prelude; 9.16/4.00 data Main.Maybe a = Nothing | Just a ; 9.16/4.00 9.16/4.00 esLtLt :: (b -> Main.Maybe a) -> Main.Maybe b -> Main.Maybe a; 9.16/4.00 esLtLt f x = gtGtEsMaybe x f; 9.16/4.00 9.16/4.00 gtGtEsMaybe :: Main.Maybe a -> (a -> Main.Maybe b) -> Main.Maybe b; 9.16/4.00 gtGtEsMaybe (Main.Just x) k = k x; 9.16/4.00 gtGtEsMaybe Main.Nothing k = Main.Nothing; 9.16/4.00 9.16/4.00 } 9.16/4.00 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (3) COR (EQUIVALENT) 9.16/4.00 Cond Reductions: 9.16/4.00 The following Function with conditions 9.16/4.00 "undefined |Falseundefined; 9.16/4.00 " 9.16/4.00 is transformed to 9.16/4.00 "undefined = undefined1; 9.16/4.00 " 9.16/4.00 "undefined0 True = undefined; 9.16/4.00 " 9.16/4.00 "undefined1 = undefined0 False; 9.16/4.00 " 9.16/4.00 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (4) 9.16/4.00 Obligation: 9.16/4.00 mainModule Main 9.16/4.00 module Main where { 9.16/4.00 import qualified Prelude; 9.16/4.00 data Main.Maybe a = Nothing | Just a ; 9.16/4.00 9.16/4.00 esLtLt :: (a -> Main.Maybe b) -> Main.Maybe a -> Main.Maybe b; 9.16/4.00 esLtLt f x = gtGtEsMaybe x f; 9.16/4.00 9.16/4.00 gtGtEsMaybe :: Main.Maybe b -> (b -> Main.Maybe a) -> Main.Maybe a; 9.16/4.00 gtGtEsMaybe (Main.Just x) k = k x; 9.16/4.00 gtGtEsMaybe Main.Nothing k = Main.Nothing; 9.16/4.00 9.16/4.00 } 9.16/4.00 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (5) Narrow (EQUIVALENT) 9.16/4.00 Haskell To QDPs 9.16/4.00 9.16/4.00 digraph dp_graph { 9.16/4.00 node [outthreshold=100, inthreshold=100];1[label="esLtLt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.16/4.00 3[label="esLtLt vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.16/4.00 4[label="esLtLt vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.16/4.00 5[label="gtGtEsMaybe vx4 vx3",fontsize=16,color="burlywood",shape="box"];11[label="vx4/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9]; 9.16/4.00 11 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.16/4.00 12[label="vx4/Just vx40",fontsize=10,color="white",style="solid",shape="box"];5 -> 12[label="",style="solid", color="burlywood", weight=9]; 9.16/4.00 12 -> 7[label="",style="solid", color="burlywood", weight=3]; 9.16/4.00 6[label="gtGtEsMaybe Nothing vx3",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.16/4.00 7[label="gtGtEsMaybe (Just vx40) vx3",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3]; 9.16/4.00 8[label="Nothing",fontsize=16,color="green",shape="box"];9[label="vx3 vx40",fontsize=16,color="green",shape="box"];9 -> 10[label="",style="dashed", color="green", weight=3]; 9.16/4.00 10[label="vx40",fontsize=16,color="green",shape="box"];} 9.16/4.00 9.16/4.00 ---------------------------------------- 9.16/4.00 9.16/4.00 (6) 9.16/4.00 YES 9.18/4.03 EOF