7.67/3.52 YES 9.33/4.00 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 9.33/4.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.33/4.00 9.33/4.00 9.33/4.00 H-Termination with start terms of the given HASKELL could be proven: 9.33/4.00 9.33/4.00 (0) HASKELL 9.33/4.00 (1) BR [EQUIVALENT, 0 ms] 9.33/4.00 (2) HASKELL 9.33/4.00 (3) COR [EQUIVALENT, 0 ms] 9.33/4.00 (4) HASKELL 9.33/4.00 (5) Narrow [EQUIVALENT, 0 ms] 9.33/4.00 (6) YES 9.33/4.00 9.33/4.00 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (0) 9.33/4.00 Obligation: 9.33/4.00 mainModule Main 9.33/4.00 module Main where { 9.33/4.00 import qualified Prelude; 9.33/4.00 data Main.WHNF a = WHNF a ; 9.33/4.00 9.33/4.00 dsEm :: (a -> b) -> a -> b; 9.33/4.00 dsEm f x = Main.seq x (f x); 9.33/4.00 9.33/4.00 enforceWHNF :: Main.WHNF a -> b -> b; 9.33/4.00 enforceWHNF (Main.WHNF x) y = y; 9.33/4.00 9.33/4.00 seq :: a -> b -> b; 9.33/4.00 seq x y = Main.enforceWHNF (Main.WHNF x) y; 9.33/4.00 9.33/4.00 } 9.33/4.00 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (1) BR (EQUIVALENT) 9.33/4.00 Replaced joker patterns by fresh variables and removed binding patterns. 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (2) 9.33/4.00 Obligation: 9.33/4.00 mainModule Main 9.33/4.00 module Main where { 9.33/4.00 import qualified Prelude; 9.33/4.00 data Main.WHNF a = WHNF a ; 9.33/4.00 9.33/4.00 dsEm :: (b -> a) -> b -> a; 9.33/4.00 dsEm f x = Main.seq x (f x); 9.33/4.00 9.33/4.00 enforceWHNF :: Main.WHNF a -> b -> b; 9.33/4.00 enforceWHNF (Main.WHNF x) y = y; 9.33/4.00 9.33/4.00 seq :: b -> a -> a; 9.33/4.00 seq x y = Main.enforceWHNF (Main.WHNF x) y; 9.33/4.00 9.33/4.00 } 9.33/4.00 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (3) COR (EQUIVALENT) 9.33/4.00 Cond Reductions: 9.33/4.00 The following Function with conditions 9.33/4.00 "undefined |Falseundefined; 9.33/4.00 " 9.33/4.00 is transformed to 9.33/4.00 "undefined = undefined1; 9.33/4.00 " 9.33/4.00 "undefined0 True = undefined; 9.33/4.00 " 9.33/4.00 "undefined1 = undefined0 False; 9.33/4.00 " 9.33/4.00 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (4) 9.33/4.00 Obligation: 9.33/4.00 mainModule Main 9.33/4.00 module Main where { 9.33/4.00 import qualified Prelude; 9.33/4.00 data Main.WHNF a = WHNF a ; 9.33/4.00 9.33/4.00 dsEm :: (a -> b) -> a -> b; 9.33/4.00 dsEm f x = Main.seq x (f x); 9.33/4.00 9.33/4.00 enforceWHNF :: Main.WHNF a -> b -> b; 9.33/4.00 enforceWHNF (Main.WHNF x) y = y; 9.33/4.00 9.33/4.00 seq :: b -> a -> a; 9.33/4.00 seq x y = Main.enforceWHNF (Main.WHNF x) y; 9.33/4.00 9.33/4.00 } 9.33/4.00 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (5) Narrow (EQUIVALENT) 9.33/4.00 Haskell To QDPs 9.33/4.00 9.33/4.00 digraph dp_graph { 9.33/4.00 node [outthreshold=100, inthreshold=100];1[label="dsEm",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 9.33/4.00 3[label="dsEm vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 9.33/4.00 4[label="dsEm vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 9.33/4.00 5[label="seq vx4 (vx3 vx4)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 9.33/4.00 6[label="enforceWHNF (WHNF vx4) (vx3 vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 9.33/4.00 7[label="vx3 vx4",fontsize=16,color="green",shape="box"];7 -> 8[label="",style="dashed", color="green", weight=3]; 9.33/4.00 8[label="vx4",fontsize=16,color="green",shape="box"];} 9.33/4.00 9.33/4.00 ---------------------------------------- 9.33/4.00 9.33/4.00 (6) 9.33/4.00 YES 9.36/4.04 EOF