8.82/3.82	YES
10.20/4.24	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.20/4.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.20/4.24	
10.20/4.24	
10.20/4.24	H-Termination with start terms of the given HASKELL could be proven:
10.20/4.24	
10.20/4.24	(0) HASKELL
10.20/4.24	(1) BR [EQUIVALENT, 0 ms]
10.20/4.24	(2) HASKELL
10.20/4.24	(3) COR [EQUIVALENT, 0 ms]
10.20/4.24	(4) HASKELL
10.20/4.24	(5) Narrow [EQUIVALENT, 12 ms]
10.20/4.24	(6) YES
10.20/4.24	
10.20/4.24	
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(0)
10.20/4.24	Obligation:
10.20/4.24	mainModule Main 
10.20/4.24	module Maybe where {
10.20/4.24	import qualified Main;
10.20/4.24	import qualified Monad;
10.20/4.24	import qualified Prelude;
10.20/4.24	}
10.20/4.24	module Main where {
10.20/4.24	import qualified Maybe;
10.20/4.24	import qualified Monad;
10.20/4.24	import qualified Prelude;
10.20/4.24	}
10.20/4.24	module Monad where {
10.20/4.24	import qualified Main;
10.20/4.24	import qualified Maybe;
10.20/4.24	import qualified Prelude;
10.20/4.24	class Monad a => MonadPlus a where {
10.20/4.24	mzero :: MonadPlus a => a b;
10.20/4.24	}
10.20/4.24	instance MonadPlus Maybe where { 
10.20/4.24	}
10.20/4.24	instance MonadPlus [] where { 
10.20/4.24	mzero = [];
10.20/4.24	}
10.20/4.24	}
10.20/4.24	
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(1) BR (EQUIVALENT)
10.20/4.24	Replaced joker patterns by fresh variables and removed binding patterns.
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(2)
10.20/4.24	Obligation:
10.20/4.24	mainModule Main 
10.20/4.24	module Maybe where {
10.20/4.24	import qualified Main;
10.20/4.24	import qualified Monad;
10.20/4.24	import qualified Prelude;
10.20/4.24	}
10.20/4.24	module Main where {
10.20/4.24	import qualified Maybe;
10.20/4.24	import qualified Monad;
10.20/4.24	import qualified Prelude;
10.20/4.24	}
10.20/4.24	module Monad where {
10.20/4.24	import qualified Main;
10.20/4.24	import qualified Maybe;
10.20/4.24	import qualified Prelude;
10.20/4.24	class Monad a => MonadPlus a where {
10.20/4.24	mzero :: MonadPlus a => a b;
10.20/4.24	}
10.20/4.24	instance MonadPlus Maybe where { 
10.20/4.24	}
10.20/4.24	instance MonadPlus [] where { 
10.20/4.24	mzero = [];
10.20/4.24	}
10.20/4.24	}
10.20/4.24	
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(3) COR (EQUIVALENT)
10.20/4.24	Cond Reductions:
10.20/4.24	The following Function with conditions
10.20/4.24	"undefined |Falseundefined;
10.20/4.24	"
10.20/4.24	is transformed to
10.20/4.24	"undefined  = undefined1;
10.20/4.24	"
10.20/4.24	"undefined0 True = undefined;
10.20/4.24	"
10.20/4.24	"undefined1  = undefined0 False;
10.20/4.24	"
10.20/4.24	
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(4)
10.20/4.24	Obligation:
10.20/4.24	mainModule Main 
10.20/4.24	module Maybe where {
10.20/4.24	import qualified Main;
10.20/4.24	import qualified Monad;
10.20/4.24	import qualified Prelude;
10.20/4.24	}
10.20/4.24	module Main where {
10.20/4.24	import qualified Maybe;
10.20/4.24	import qualified Monad;
10.20/4.24	import qualified Prelude;
10.20/4.24	}
10.20/4.24	module Monad where {
10.20/4.24	import qualified Main;
10.20/4.24	import qualified Maybe;
10.20/4.24	import qualified Prelude;
10.20/4.24	class Monad a => MonadPlus a where {
10.20/4.24	mzero :: MonadPlus a => a b;
10.20/4.24	}
10.20/4.24	instance MonadPlus Maybe where { 
10.20/4.24	}
10.20/4.24	instance MonadPlus [] where { 
10.20/4.24	mzero = [];
10.20/4.24	}
10.20/4.24	}
10.20/4.24	
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(5) Narrow (EQUIVALENT)
10.20/4.24	Haskell To QDPs
10.20/4.24	
10.20/4.24	digraph dp_graph {
10.20/4.24	node [outthreshold=100, inthreshold=100];1[label="Monad.mzero",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
10.20/4.24	3[label="[]",fontsize=16,color="green",shape="box"];}
10.20/4.24	
10.20/4.24	----------------------------------------
10.20/4.24	
10.20/4.24	(6)
10.20/4.24	YES
10.28/4.30	EOF