45.01/31.76	MAYBE
47.00/32.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
47.00/32.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
47.00/32.34	
47.00/32.34	
47.00/32.34	H-Termination with start terms of the given HASKELL could not be shown:
47.00/32.34	
47.00/32.34	(0) HASKELL
47.00/32.34	(1) LR [EQUIVALENT, 0 ms]
47.00/32.34	(2) HASKELL
47.00/32.34	(3) IPR [EQUIVALENT, 0 ms]
47.00/32.34	(4) HASKELL
47.00/32.34	(5) BR [EQUIVALENT, 0 ms]
47.00/32.34	(6) HASKELL
47.00/32.34	(7) COR [EQUIVALENT, 0 ms]
47.00/32.34	(8) HASKELL
47.00/32.34	
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(0)
47.00/32.34	Obligation:
47.00/32.34	mainModule Main 
47.00/32.34	module Maybe where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Main where {
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Monad where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Prelude;
47.00/32.34	mapAndUnzipM :: Monad c => (a  ->  c (b,d))  ->  [a]  ->  c ([b],[d]);
47.00/32.34	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
47.00/32.34	
47.00/32.34	}
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(1) LR (EQUIVALENT)
47.00/32.34	Lambda Reductions:
47.00/32.34	The following Lambda expression
47.00/32.34	"\(a,b)~(as,bs)->(a : as,b : bs)"
47.00/32.34	is transformed to
47.00/32.34	"unzip0 (a,b) ~(as,bs) = (a : as,b : bs);
47.00/32.34	"
47.00/32.34	The following Lambda expression
47.00/32.34	"\xs->return (x : xs)"
47.00/32.34	is transformed to
47.00/32.34	"sequence0 x xs = return (x : xs);
47.00/32.34	"
47.00/32.34	The following Lambda expression
47.00/32.34	"\x->sequence cs >>= sequence0 x"
47.00/32.34	is transformed to
47.00/32.34	"sequence1 cs x = sequence cs >>= sequence0 x;
47.00/32.34	"
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(2)
47.00/32.34	Obligation:
47.00/32.34	mainModule Main 
47.00/32.34	module Maybe where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Main where {
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Monad where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Prelude;
47.00/32.34	mapAndUnzipM :: Monad b => (a  ->  b (d,c))  ->  [a]  ->  b ([d],[c]);
47.00/32.34	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
47.00/32.34	
47.00/32.34	}
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(3) IPR (EQUIVALENT)
47.00/32.34	IrrPat Reductions:
47.00/32.34	The variables of the following irrefutable Pattern
47.00/32.34	"~(as,bs)"
47.00/32.34	are replaced by calls to these functions
47.00/32.34	"unzip00 (as,bs) = as;
47.00/32.34	"
47.00/32.34	"unzip01 (as,bs) = bs;
47.00/32.34	"
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(4)
47.00/32.34	Obligation:
47.00/32.34	mainModule Main 
47.00/32.34	module Maybe where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Main where {
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Monad where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Prelude;
47.00/32.34	mapAndUnzipM :: Monad c => (b  ->  c (a,d))  ->  [b]  ->  c ([a],[d]);
47.00/32.34	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
47.00/32.34	
47.00/32.34	}
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(5) BR (EQUIVALENT)
47.00/32.34	Replaced joker patterns by fresh variables and removed binding patterns.
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(6)
47.00/32.34	Obligation:
47.00/32.34	mainModule Main 
47.00/32.34	module Maybe where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Main where {
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Monad where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Prelude;
47.00/32.34	mapAndUnzipM :: Monad d => (a  ->  d (c,b))  ->  [a]  ->  d ([c],[b]);
47.00/32.34	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
47.00/32.34	
47.00/32.34	}
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(7) COR (EQUIVALENT)
47.00/32.34	Cond Reductions:
47.00/32.34	The following Function with conditions
47.00/32.34	"undefined |Falseundefined;
47.00/32.34	"
47.00/32.34	is transformed to
47.00/32.34	"undefined  = undefined1;
47.00/32.34	"
47.00/32.34	"undefined0 True = undefined;
47.00/32.34	"
47.00/32.34	"undefined1  = undefined0 False;
47.00/32.34	"
47.00/32.34	
47.00/32.34	----------------------------------------
47.00/32.34	
47.00/32.34	(8)
47.00/32.34	Obligation:
47.00/32.34	mainModule Main 
47.00/32.34	module Maybe where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Main where {
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Monad;
47.00/32.34	import qualified Prelude;
47.00/32.34	}
47.00/32.34	module Monad where {
47.00/32.34	import qualified Main;
47.00/32.34	import qualified Maybe;
47.00/32.34	import qualified Prelude;
47.00/32.34	mapAndUnzipM :: Monad d => (c  ->  d (a,b))  ->  [c]  ->  d ([a],[b]);
47.00/32.34	mapAndUnzipM f xs = sequence (map f xs) >>= return . unzip;
47.00/32.34	
47.00/32.34	}
47.00/32.37	EOF