159.76/134.91	MAYBE
161.58/135.43	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
161.58/135.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
161.58/135.43	
161.58/135.43	
161.58/135.43	H-Termination with start terms of the given HASKELL could not be shown:
161.58/135.43	
161.58/135.43	(0) HASKELL
161.58/135.43	(1) BR [EQUIVALENT, 0 ms]
161.58/135.43	(2) HASKELL
161.58/135.43	(3) COR [EQUIVALENT, 20 ms]
161.58/135.43	(4) HASKELL
161.58/135.43	(5) LetRed [EQUIVALENT, 0 ms]
161.58/135.43	(6) HASKELL
161.58/135.43	
161.58/135.43	
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(0)
161.58/135.43	Obligation:
161.58/135.43	mainModule Main 
161.58/135.43	module Maybe where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	module List where {
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	nub :: Eq a => [a]  ->  [a];
161.58/135.43	nub l = nub' l [] where { 
161.58/135.43	nub' [] _ = [];
161.58/135.43	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
161.58/135.43	 | otherwise = x : nub' xs (x : ls);
161.58/135.43	 };
161.58/135.43	
161.58/135.43	}
161.58/135.43	module Main where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(1) BR (EQUIVALENT)
161.58/135.43	Replaced joker patterns by fresh variables and removed binding patterns.
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(2)
161.58/135.43	Obligation:
161.58/135.43	mainModule Main 
161.58/135.43	module Maybe where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	module List where {
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	nub :: Eq a => [a]  ->  [a];
161.58/135.43	nub l = nub' l [] where { 
161.58/135.43	nub' [] wu = [];
161.58/135.43	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
161.58/135.43	 | otherwise = x : nub' xs (x : ls);
161.58/135.43	 };
161.58/135.43	
161.58/135.43	}
161.58/135.43	module Main where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(3) COR (EQUIVALENT)
161.58/135.43	Cond Reductions:
161.58/135.43	The following Function with conditions
161.58/135.43	"undefined |Falseundefined;
161.58/135.43	"
161.58/135.43	is transformed to
161.58/135.43	"undefined  = undefined1;
161.58/135.43	"
161.58/135.43	"undefined0 True = undefined;
161.58/135.43	"
161.58/135.43	"undefined1  = undefined0 False;
161.58/135.43	"
161.58/135.43	The following Function with conditions
161.58/135.43	"nub' [] wu = [];
161.58/135.43	nub' (x : xs) ls|x `elem` lsnub' xs ls|otherwisex : nub' xs (x : ls);
161.58/135.43	"
161.58/135.43	is transformed to
161.58/135.43	"nub' [] wu = nub'3 [] wu;
161.58/135.43	nub' (x : xs) ls = nub'2 (x : xs) ls;
161.58/135.43	"
161.58/135.43	"nub'1 x xs ls True = nub' xs ls;
161.58/135.43	nub'1 x xs ls False = nub'0 x xs ls otherwise;
161.58/135.43	"
161.58/135.43	"nub'0 x xs ls True = x : nub' xs (x : ls);
161.58/135.43	"
161.58/135.43	"nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
161.58/135.43	"
161.58/135.43	"nub'3 [] wu = [];
161.58/135.43	nub'3 wx wy = nub'2 wx wy;
161.58/135.43	"
161.58/135.43	
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(4)
161.58/135.43	Obligation:
161.58/135.43	mainModule Main 
161.58/135.43	module Maybe where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	module List where {
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	nub :: Eq a => [a]  ->  [a];
161.58/135.43	nub l = nub' l [] where { 
161.58/135.43	nub' [] wu = nub'3 [] wu;
161.58/135.43	nub' (x : xs) ls = nub'2 (x : xs) ls;
161.58/135.43	nub'0 x xs ls True = x : nub' xs (x : ls);
161.58/135.43	nub'1 x xs ls True = nub' xs ls;
161.58/135.43	nub'1 x xs ls False = nub'0 x xs ls otherwise;
161.58/135.43	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
161.58/135.43	nub'3 [] wu = [];
161.58/135.43	nub'3 wx wy = nub'2 wx wy;
161.58/135.43	 };
161.58/135.43	
161.58/135.43	}
161.58/135.43	module Main where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(5) LetRed (EQUIVALENT)
161.58/135.43	Let/Where Reductions:
161.58/135.43	The bindings of the following Let/Where expression
161.58/135.43	"nub' l [] where {
161.58/135.43	nub' [] wu = nub'3 [] wu;
161.58/135.43	nub' (x : xs) ls = nub'2 (x : xs) ls;
161.58/135.43	;
161.58/135.43	nub'0 x xs ls True = x : nub' xs (x : ls);
161.58/135.43	;
161.58/135.43	nub'1 x xs ls True = nub' xs ls;
161.58/135.43	nub'1 x xs ls False = nub'0 x xs ls otherwise;
161.58/135.43	;
161.58/135.43	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
161.58/135.43	;
161.58/135.43	nub'3 [] wu = [];
161.58/135.43	nub'3 wx wy = nub'2 wx wy;
161.58/135.43	} 
161.58/135.43	"
161.58/135.43	are unpacked to the following functions on top level
161.58/135.43	"nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
161.58/135.43	"
161.58/135.43	"nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
161.58/135.43	"
161.58/135.43	"nubNub' [] wu = nubNub'3 [] wu;
161.58/135.43	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
161.58/135.43	"
161.58/135.43	"nubNub'3 [] wu = [];
161.58/135.43	nubNub'3 wx wy = nubNub'2 wx wy;
161.58/135.43	"
161.58/135.43	"nubNub'1 x xs ls True = nubNub' xs ls;
161.58/135.43	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
161.58/135.43	"
161.58/135.43	
161.58/135.43	----------------------------------------
161.58/135.43	
161.58/135.43	(6)
161.58/135.43	Obligation:
161.58/135.43	mainModule Main 
161.58/135.43	module Maybe where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.58/135.43	module List where {
161.58/135.43	import qualified Main;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	nub :: Eq a => [a]  ->  [a];
161.58/135.43	nub l = nubNub' l [];
161.58/135.43	
161.58/135.43	nubNub' [] wu = nubNub'3 [] wu;
161.58/135.43	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
161.58/135.43	
161.58/135.43	nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
161.58/135.43	
161.58/135.43	nubNub'1 x xs ls True = nubNub' xs ls;
161.58/135.43	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
161.58/135.43	
161.58/135.43	nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
161.58/135.43	
161.58/135.43	nubNub'3 [] wu = [];
161.58/135.43	nubNub'3 wx wy = nubNub'2 wx wy;
161.58/135.43	
161.58/135.43	}
161.58/135.43	module Main where {
161.58/135.43	import qualified List;
161.58/135.43	import qualified Maybe;
161.58/135.43	import qualified Prelude;
161.58/135.43	}
161.68/135.48	EOF