7.78/3.44 YES 9.37/3.88 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.37/3.88 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.37/3.88 9.37/3.88 9.37/3.88 H-Termination with start terms of the given HASKELL could be proven: 9.37/3.88 9.37/3.88 (0) HASKELL 9.37/3.88 (1) BR [EQUIVALENT, 0 ms] 9.37/3.88 (2) HASKELL 9.37/3.88 (3) COR [EQUIVALENT, 0 ms] 9.37/3.88 (4) HASKELL 9.37/3.88 (5) Narrow [EQUIVALENT, 0 ms] 9.37/3.88 (6) YES 9.37/3.88 9.37/3.88 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (0) 9.37/3.88 Obligation: 9.37/3.88 mainModule Main 9.37/3.88 module Main where { 9.37/3.88 import qualified Prelude; 9.37/3.88 data Main.Maybe a = Nothing | Just a ; 9.37/3.88 9.37/3.88 gtGtEsMaybe :: Main.Maybe a -> (a -> Main.Maybe b) -> Main.Maybe b; 9.37/3.88 gtGtEsMaybe (Main.Just x) k = k x; 9.37/3.88 gtGtEsMaybe Main.Nothing k = Main.Nothing; 9.37/3.88 9.37/3.88 } 9.37/3.88 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (1) BR (EQUIVALENT) 9.37/3.88 Replaced joker patterns by fresh variables and removed binding patterns. 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (2) 9.37/3.88 Obligation: 9.37/3.88 mainModule Main 9.37/3.88 module Main where { 9.37/3.88 import qualified Prelude; 9.37/3.88 data Main.Maybe a = Nothing | Just a ; 9.37/3.88 9.37/3.88 gtGtEsMaybe :: Main.Maybe a -> (a -> Main.Maybe b) -> Main.Maybe b; 9.37/3.88 gtGtEsMaybe (Main.Just x) k = k x; 9.37/3.88 gtGtEsMaybe Main.Nothing k = Main.Nothing; 9.37/3.88 9.37/3.88 } 9.37/3.88 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (3) COR (EQUIVALENT) 9.37/3.88 Cond Reductions: 9.37/3.88 The following Function with conditions 9.37/3.88 "undefined |Falseundefined; 9.37/3.88 " 9.37/3.88 is transformed to 9.37/3.88 "undefined = undefined1; 9.37/3.88 " 9.37/3.88 "undefined0 True = undefined; 9.37/3.88 " 9.37/3.88 "undefined1 = undefined0 False; 9.37/3.88 " 9.37/3.88 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (4) 9.37/3.88 Obligation: 9.37/3.88 mainModule Main 9.37/3.88 module Main where { 9.37/3.88 import qualified Prelude; 9.37/3.88 data Main.Maybe a = Nothing | Just a ; 9.37/3.88 9.37/3.88 gtGtEsMaybe :: Main.Maybe b -> (b -> Main.Maybe a) -> Main.Maybe a; 9.37/3.88 gtGtEsMaybe (Main.Just x) k = k x; 9.37/3.88 gtGtEsMaybe Main.Nothing k = Main.Nothing; 9.37/3.88 9.37/3.88 } 9.37/3.88 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (5) Narrow (EQUIVALENT) 9.37/3.88 Haskell To QDPs 9.37/3.88 9.37/3.88 digraph dp_graph { 9.37/3.88 node [outthreshold=100, inthreshold=100];1[label="gtGtEsMaybe",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.37/3.88 3[label="gtGtEsMaybe vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.37/3.88 4[label="gtGtEsMaybe vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];10[label="vx3/Nothing",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9]; 9.37/3.88 10 -> 5[label="",style="solid", color="burlywood", weight=3]; 9.37/3.88 11[label="vx3/Just vx30",fontsize=10,color="white",style="solid",shape="box"];4 -> 11[label="",style="solid", color="burlywood", weight=9]; 9.37/3.88 11 -> 6[label="",style="solid", color="burlywood", weight=3]; 9.37/3.88 5[label="gtGtEsMaybe Nothing vx4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 9.37/3.88 6[label="gtGtEsMaybe (Just vx30) vx4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 9.37/3.88 7[label="Nothing",fontsize=16,color="green",shape="box"];8[label="vx4 vx30",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3]; 9.37/3.88 9[label="vx30",fontsize=16,color="green",shape="box"];} 9.37/3.88 9.37/3.88 ---------------------------------------- 9.37/3.88 9.37/3.88 (6) 9.37/3.88 YES 9.37/3.92 EOF