8.74/3.86	YES
10.91/4.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.91/4.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.91/4.39	
10.91/4.39	
10.91/4.39	H-Termination with start terms of the given HASKELL could be proven:
10.91/4.39	
10.91/4.39	(0) HASKELL
10.91/4.39	(1) IFR [EQUIVALENT, 0 ms]
10.91/4.39	(2) HASKELL
10.91/4.39	(3) BR [EQUIVALENT, 0 ms]
10.91/4.39	(4) HASKELL
10.91/4.39	(5) COR [EQUIVALENT, 0 ms]
10.91/4.39	(6) HASKELL
10.91/4.39	(7) Narrow [EQUIVALENT, 20 ms]
10.91/4.39	(8) YES
10.91/4.39	
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(0)
10.91/4.39	Obligation:
10.91/4.39	mainModule Main 
10.91/4.39	module Maybe where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Main where {
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Monad where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Prelude;
10.91/4.39	when :: Monad a => Bool  ->  a ()  ->  a ();
10.91/4.39	when p s =  if p then s else return ();
10.91/4.39	
10.91/4.39	}
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(1) IFR (EQUIVALENT)
10.91/4.39	If Reductions:
10.91/4.39	The following If expression
10.91/4.39	"if p then s else return ()"
10.91/4.39	is transformed to
10.91/4.39	"when0 s True = s;
10.91/4.39	when0 s False = return ();
10.91/4.39	"
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(2)
10.91/4.39	Obligation:
10.91/4.39	mainModule Main 
10.91/4.39	module Maybe where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Main where {
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Monad where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Prelude;
10.91/4.39	when :: Monad a => Bool  ->  a ()  ->  a ();
10.91/4.39	when p s = when0 s p;
10.91/4.39	
10.91/4.39	when0 s True = s;
10.91/4.39	when0 s False = return ();
10.91/4.39	
10.91/4.39	}
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(3) BR (EQUIVALENT)
10.91/4.39	Replaced joker patterns by fresh variables and removed binding patterns.
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(4)
10.91/4.39	Obligation:
10.91/4.39	mainModule Main 
10.91/4.39	module Maybe where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Main where {
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Monad where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Prelude;
10.91/4.39	when :: Monad a => Bool  ->  a ()  ->  a ();
10.91/4.39	when p s = when0 s p;
10.91/4.39	
10.91/4.39	when0 s True = s;
10.91/4.39	when0 s False = return ();
10.91/4.39	
10.91/4.39	}
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(5) COR (EQUIVALENT)
10.91/4.39	Cond Reductions:
10.91/4.39	The following Function with conditions
10.91/4.39	"undefined |Falseundefined;
10.91/4.39	"
10.91/4.39	is transformed to
10.91/4.39	"undefined  = undefined1;
10.91/4.39	"
10.91/4.39	"undefined0 True = undefined;
10.91/4.39	"
10.91/4.39	"undefined1  = undefined0 False;
10.91/4.39	"
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(6)
10.91/4.39	Obligation:
10.91/4.39	mainModule Main 
10.91/4.39	module Maybe where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Main where {
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Monad;
10.91/4.39	import qualified Prelude;
10.91/4.39	}
10.91/4.39	module Monad where {
10.91/4.39	import qualified Main;
10.91/4.39	import qualified Maybe;
10.91/4.39	import qualified Prelude;
10.91/4.39	when :: Monad a => Bool  ->  a ()  ->  a ();
10.91/4.39	when p s = when0 s p;
10.91/4.39	
10.91/4.39	when0 s True = s;
10.91/4.39	when0 s False = return ();
10.91/4.39	
10.91/4.39	}
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(7) Narrow (EQUIVALENT)
10.91/4.39	Haskell To QDPs
10.91/4.39	
10.91/4.39	digraph dp_graph {
10.91/4.39	node [outthreshold=100, inthreshold=100];1[label="Monad.when",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.91/4.39	3[label="Monad.when vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.91/4.39	4[label="Monad.when vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.91/4.39	5[label="Monad.when0 vy4 vy3",fontsize=16,color="burlywood",shape="box"];11[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
10.91/4.39	11 -> 6[label="",style="solid", color="burlywood", weight=3];
10.91/4.39	12[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 12[label="",style="solid", color="burlywood", weight=9];
10.91/4.39	12 -> 7[label="",style="solid", color="burlywood", weight=3];
10.91/4.39	6[label="Monad.when0 vy4 False",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.91/4.39	7[label="Monad.when0 vy4 True",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.91/4.39	8[label="return ()",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
10.91/4.39	9[label="vy4",fontsize=16,color="green",shape="box"];10[label="Just ()",fontsize=16,color="green",shape="box"];}
10.91/4.39	
10.91/4.39	----------------------------------------
10.91/4.39	
10.91/4.39	(8)
10.91/4.39	YES
10.91/4.43	EOF