8.83/3.85	YES
10.65/4.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.65/4.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.65/4.34	
10.65/4.34	
10.65/4.34	H-Termination with start terms of the given HASKELL could be proven:
10.65/4.34	
10.65/4.34	(0) HASKELL
10.65/4.34	(1) BR [EQUIVALENT, 0 ms]
10.65/4.34	(2) HASKELL
10.65/4.34	(3) COR [EQUIVALENT, 0 ms]
10.65/4.34	(4) HASKELL
10.65/4.34	(5) Narrow [EQUIVALENT, 25 ms]
10.65/4.34	(6) YES
10.65/4.34	
10.65/4.34	
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(0)
10.65/4.34	Obligation:
10.65/4.34	mainModule Main 
10.65/4.34	module Maybe where {
10.65/4.34	import qualified Main;
10.65/4.34	import qualified Monad;
10.65/4.34	import qualified Prelude;
10.65/4.34	}
10.65/4.34	module Main where {
10.65/4.34	import qualified Maybe;
10.65/4.34	import qualified Monad;
10.65/4.34	import qualified Prelude;
10.65/4.34	}
10.65/4.34	module Monad where {
10.65/4.34	import qualified Main;
10.65/4.34	import qualified Maybe;
10.65/4.34	import qualified Prelude;
10.65/4.34	class Monad a => MonadPlus a where {
10.65/4.34	mzero :: MonadPlus a => a b;
10.65/4.34	}
10.65/4.34	instance MonadPlus Maybe where { 
10.65/4.34	mzero = Nothing;
10.65/4.34	}
10.65/4.34	instance MonadPlus [] where { 
10.65/4.34	}
10.65/4.34	}
10.65/4.34	
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(1) BR (EQUIVALENT)
10.65/4.34	Replaced joker patterns by fresh variables and removed binding patterns.
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(2)
10.65/4.34	Obligation:
10.65/4.34	mainModule Main 
10.65/4.34	module Maybe where {
10.65/4.34	import qualified Main;
10.65/4.34	import qualified Monad;
10.65/4.34	import qualified Prelude;
10.65/4.34	}
10.65/4.34	module Main where {
10.65/4.34	import qualified Maybe;
10.65/4.34	import qualified Monad;
10.65/4.34	import qualified Prelude;
10.65/4.34	}
10.65/4.34	module Monad where {
10.65/4.34	import qualified Main;
10.65/4.34	import qualified Maybe;
10.65/4.34	import qualified Prelude;
10.65/4.34	class Monad a => MonadPlus a where {
10.65/4.34	mzero :: MonadPlus a => a b;
10.65/4.34	}
10.65/4.34	instance MonadPlus Maybe where { 
10.65/4.34	mzero = Nothing;
10.65/4.34	}
10.65/4.34	instance MonadPlus [] where { 
10.65/4.34	}
10.65/4.34	}
10.65/4.34	
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(3) COR (EQUIVALENT)
10.65/4.34	Cond Reductions:
10.65/4.34	The following Function with conditions
10.65/4.34	"undefined |Falseundefined;
10.65/4.34	"
10.65/4.34	is transformed to
10.65/4.34	"undefined  = undefined1;
10.65/4.34	"
10.65/4.34	"undefined0 True = undefined;
10.65/4.34	"
10.65/4.34	"undefined1  = undefined0 False;
10.65/4.34	"
10.65/4.34	
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(4)
10.65/4.34	Obligation:
10.65/4.34	mainModule Main 
10.65/4.34	module Maybe where {
10.65/4.34	import qualified Main;
10.65/4.34	import qualified Monad;
10.65/4.34	import qualified Prelude;
10.65/4.34	}
10.65/4.34	module Main where {
10.65/4.34	import qualified Maybe;
10.65/4.34	import qualified Monad;
10.65/4.34	import qualified Prelude;
10.65/4.34	}
10.65/4.34	module Monad where {
10.65/4.34	import qualified Main;
10.65/4.34	import qualified Maybe;
10.65/4.34	import qualified Prelude;
10.65/4.34	class Monad a => MonadPlus a where {
10.65/4.34	mzero :: MonadPlus a => a b;
10.65/4.34	}
10.65/4.34	instance MonadPlus Maybe where { 
10.65/4.34	mzero = Nothing;
10.65/4.34	}
10.65/4.34	instance MonadPlus [] where { 
10.65/4.34	}
10.65/4.34	}
10.65/4.34	
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(5) Narrow (EQUIVALENT)
10.65/4.34	Haskell To QDPs
10.65/4.34	
10.65/4.34	digraph dp_graph {
10.65/4.34	node [outthreshold=100, inthreshold=100];1[label="Monad.mzero",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
10.65/4.34	3[label="Nothing",fontsize=16,color="green",shape="box"];}
10.65/4.34	
10.65/4.34	----------------------------------------
10.65/4.34	
10.65/4.34	(6)
10.65/4.34	YES
10.73/6.57	EOF