9.03/3.93	YES
10.67/4.41	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
10.67/4.41	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.67/4.41	
10.67/4.41	
10.67/4.41	H-Termination with start terms of the given HASKELL could be proven:
10.67/4.41	
10.67/4.41	(0) HASKELL
10.67/4.41	(1) BR [EQUIVALENT, 0 ms]
10.67/4.41	(2) HASKELL
10.67/4.41	(3) COR [EQUIVALENT, 0 ms]
10.67/4.41	(4) HASKELL
10.67/4.41	(5) Narrow [EQUIVALENT, 21 ms]
10.67/4.41	(6) YES
10.67/4.41	
10.67/4.41	
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(0)
10.67/4.41	Obligation:
10.67/4.41	mainModule Main 
10.67/4.41	module Maybe where {
10.67/4.41	import qualified Main;
10.67/4.41	import qualified Monad;
10.67/4.41	import qualified Prelude;
10.67/4.41	}
10.67/4.41	module Main where {
10.67/4.41	import qualified Maybe;
10.67/4.41	import qualified Monad;
10.67/4.41	import qualified Prelude;
10.67/4.41	}
10.67/4.41	module Monad where {
10.67/4.41	import qualified Main;
10.67/4.41	import qualified Maybe;
10.67/4.41	import qualified Prelude;
10.67/4.41	class Monad a => MonadPlus a where {
10.67/4.41	mplus :: MonadPlus a => a b  ->  a b  ->  a b;
10.67/4.41	}
10.67/4.41	instance MonadPlus Maybe where { 
10.67/4.41	mplus Nothing ys = ys;
10.67/4.41	mplus xs _ys = xs;
10.67/4.41	}
10.67/4.41	instance MonadPlus [] where { 
10.67/4.41	}
10.67/4.41	}
10.67/4.41	
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(1) BR (EQUIVALENT)
10.67/4.41	Replaced joker patterns by fresh variables and removed binding patterns.
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(2)
10.67/4.41	Obligation:
10.67/4.41	mainModule Main 
10.67/4.41	module Maybe where {
10.67/4.41	import qualified Main;
10.67/4.41	import qualified Monad;
10.67/4.41	import qualified Prelude;
10.67/4.41	}
10.67/4.41	module Main where {
10.67/4.41	import qualified Maybe;
10.67/4.41	import qualified Monad;
10.67/4.41	import qualified Prelude;
10.67/4.41	}
10.67/4.41	module Monad where {
10.67/4.41	import qualified Main;
10.67/4.41	import qualified Maybe;
10.67/4.41	import qualified Prelude;
10.67/4.41	class Monad a => MonadPlus a where {
10.67/4.41	mplus :: MonadPlus a => a b  ->  a b  ->  a b;
10.67/4.41	}
10.67/4.41	instance MonadPlus Maybe where { 
10.67/4.41	mplus Nothing ys = ys;
10.67/4.41	mplus xs _ys = xs;
10.67/4.41	}
10.67/4.41	instance MonadPlus [] where { 
10.67/4.41	}
10.67/4.41	}
10.67/4.41	
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(3) COR (EQUIVALENT)
10.67/4.41	Cond Reductions:
10.67/4.41	The following Function with conditions
10.67/4.41	"undefined |Falseundefined;
10.67/4.41	"
10.67/4.41	is transformed to
10.67/4.41	"undefined  = undefined1;
10.67/4.41	"
10.67/4.41	"undefined0 True = undefined;
10.67/4.41	"
10.67/4.41	"undefined1  = undefined0 False;
10.67/4.41	"
10.67/4.41	
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(4)
10.67/4.41	Obligation:
10.67/4.41	mainModule Main 
10.67/4.41	module Maybe where {
10.67/4.41	import qualified Main;
10.67/4.41	import qualified Monad;
10.67/4.41	import qualified Prelude;
10.67/4.41	}
10.67/4.41	module Main where {
10.67/4.41	import qualified Maybe;
10.67/4.41	import qualified Monad;
10.67/4.41	import qualified Prelude;
10.67/4.41	}
10.67/4.41	module Monad where {
10.67/4.41	import qualified Main;
10.67/4.41	import qualified Maybe;
10.67/4.41	import qualified Prelude;
10.67/4.41	class Monad a => MonadPlus a where {
10.67/4.41	mplus :: MonadPlus a => a b  ->  a b  ->  a b;
10.67/4.41	}
10.67/4.41	instance MonadPlus Maybe where { 
10.67/4.41	mplus Nothing ys = ys;
10.67/4.41	mplus xs _ys = xs;
10.67/4.41	}
10.67/4.41	instance MonadPlus [] where { 
10.67/4.41	}
10.67/4.41	}
10.67/4.41	
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(5) Narrow (EQUIVALENT)
10.67/4.41	Haskell To QDPs
10.67/4.41	
10.67/4.41	digraph dp_graph {
10.67/4.41	node [outthreshold=100, inthreshold=100];1[label="Monad.mplus",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.67/4.41	3[label="Monad.mplus vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.67/4.41	4[label="Monad.mplus vy3 vy4",fontsize=16,color="burlywood",shape="triangle"];9[label="vy3/Nothing",fontsize=10,color="white",style="solid",shape="box"];4 -> 9[label="",style="solid", color="burlywood", weight=9];
10.67/4.41	9 -> 5[label="",style="solid", color="burlywood", weight=3];
10.67/4.41	10[label="vy3/Just vy30",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9];
10.67/4.41	10 -> 6[label="",style="solid", color="burlywood", weight=3];
10.67/4.41	5[label="Monad.mplus Nothing vy4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
10.67/4.41	6[label="Monad.mplus (Just vy30) vy4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.67/4.41	7[label="vy4",fontsize=16,color="green",shape="box"];8[label="Just vy30",fontsize=16,color="green",shape="box"];}
10.67/4.41	
10.67/4.41	----------------------------------------
10.67/4.41	
10.67/4.41	(6)
10.67/4.41	YES
10.89/4.45	EOF