98.70/70.31	MAYBE
100.22/70.82	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
100.22/70.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
100.22/70.82	
100.22/70.82	
100.22/70.82	H-Termination with start terms of the given HASKELL could not be shown:
100.22/70.82	
100.22/70.82	(0) HASKELL
100.22/70.82	(1) BR [EQUIVALENT, 0 ms]
100.22/70.82	(2) HASKELL
100.22/70.82	(3) COR [EQUIVALENT, 27 ms]
100.22/70.82	(4) HASKELL
100.22/70.82	(5) LetRed [EQUIVALENT, 0 ms]
100.22/70.82	(6) HASKELL
100.22/70.82	
100.22/70.82	
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(0)
100.22/70.82	Obligation:
100.22/70.82	mainModule Main 
100.22/70.82	module Maybe where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	module List where {
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	nub :: Eq a => [a]  ->  [a];
100.22/70.82	nub l = nub' l [] where { 
100.22/70.82	nub' [] _ = [];
100.22/70.82	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
100.22/70.82	 | otherwise = x : nub' xs (x : ls);
100.22/70.82	 };
100.22/70.82	
100.22/70.82	}
100.22/70.82	module Main where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(1) BR (EQUIVALENT)
100.22/70.82	Replaced joker patterns by fresh variables and removed binding patterns.
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(2)
100.22/70.82	Obligation:
100.22/70.82	mainModule Main 
100.22/70.82	module Maybe where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	module List where {
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	nub :: Eq a => [a]  ->  [a];
100.22/70.82	nub l = nub' l [] where { 
100.22/70.82	nub' [] wu = [];
100.22/70.82	nub' (x : xs) ls  | x `elem` ls = nub' xs ls
100.22/70.82	 | otherwise = x : nub' xs (x : ls);
100.22/70.82	 };
100.22/70.82	
100.22/70.82	}
100.22/70.82	module Main where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(3) COR (EQUIVALENT)
100.22/70.82	Cond Reductions:
100.22/70.82	The following Function with conditions
100.22/70.82	"undefined |Falseundefined;
100.22/70.82	"
100.22/70.82	is transformed to
100.22/70.82	"undefined  = undefined1;
100.22/70.82	"
100.22/70.82	"undefined0 True = undefined;
100.22/70.82	"
100.22/70.82	"undefined1  = undefined0 False;
100.22/70.82	"
100.22/70.82	The following Function with conditions
100.22/70.82	"nub' [] wu = [];
100.22/70.82	nub' (x : xs) ls|x `elem` lsnub' xs ls|otherwisex : nub' xs (x : ls);
100.22/70.82	"
100.22/70.82	is transformed to
100.22/70.82	"nub' [] wu = nub'3 [] wu;
100.22/70.82	nub' (x : xs) ls = nub'2 (x : xs) ls;
100.22/70.82	"
100.22/70.82	"nub'0 x xs ls True = x : nub' xs (x : ls);
100.22/70.82	"
100.22/70.82	"nub'1 x xs ls True = nub' xs ls;
100.22/70.82	nub'1 x xs ls False = nub'0 x xs ls otherwise;
100.22/70.82	"
100.22/70.82	"nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
100.22/70.82	"
100.22/70.82	"nub'3 [] wu = [];
100.22/70.82	nub'3 wx wy = nub'2 wx wy;
100.22/70.82	"
100.22/70.82	
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(4)
100.22/70.82	Obligation:
100.22/70.82	mainModule Main 
100.22/70.82	module Maybe where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	module List where {
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	nub :: Eq a => [a]  ->  [a];
100.22/70.82	nub l = nub' l [] where { 
100.22/70.82	nub' [] wu = nub'3 [] wu;
100.22/70.82	nub' (x : xs) ls = nub'2 (x : xs) ls;
100.22/70.82	nub'0 x xs ls True = x : nub' xs (x : ls);
100.22/70.82	nub'1 x xs ls True = nub' xs ls;
100.22/70.82	nub'1 x xs ls False = nub'0 x xs ls otherwise;
100.22/70.82	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
100.22/70.82	nub'3 [] wu = [];
100.22/70.82	nub'3 wx wy = nub'2 wx wy;
100.22/70.82	 };
100.22/70.82	
100.22/70.82	}
100.22/70.82	module Main where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(5) LetRed (EQUIVALENT)
100.22/70.82	Let/Where Reductions:
100.22/70.82	The bindings of the following Let/Where expression
100.22/70.82	"nub' l [] where {
100.22/70.82	nub' [] wu = nub'3 [] wu;
100.22/70.82	nub' (x : xs) ls = nub'2 (x : xs) ls;
100.22/70.82	;
100.22/70.82	nub'0 x xs ls True = x : nub' xs (x : ls);
100.22/70.82	;
100.22/70.82	nub'1 x xs ls True = nub' xs ls;
100.22/70.82	nub'1 x xs ls False = nub'0 x xs ls otherwise;
100.22/70.82	;
100.22/70.82	nub'2 (x : xs) ls = nub'1 x xs ls (x `elem` ls);
100.22/70.82	;
100.22/70.82	nub'3 [] wu = [];
100.22/70.82	nub'3 wx wy = nub'2 wx wy;
100.22/70.82	} 
100.22/70.82	"
100.22/70.82	are unpacked to the following functions on top level
100.22/70.82	"nubNub'3 [] wu = [];
100.22/70.82	nubNub'3 wx wy = nubNub'2 wx wy;
100.22/70.82	"
100.22/70.82	"nubNub'1 x xs ls True = nubNub' xs ls;
100.22/70.82	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
100.22/70.82	"
100.22/70.82	"nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
100.22/70.82	"
100.22/70.82	"nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
100.22/70.82	"
100.22/70.82	"nubNub' [] wu = nubNub'3 [] wu;
100.22/70.82	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
100.22/70.82	"
100.22/70.82	
100.22/70.82	----------------------------------------
100.22/70.82	
100.22/70.82	(6)
100.22/70.82	Obligation:
100.22/70.82	mainModule Main 
100.22/70.82	module Maybe where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.22/70.82	module List where {
100.22/70.82	import qualified Main;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	nub :: Eq a => [a]  ->  [a];
100.22/70.82	nub l = nubNub' l [];
100.22/70.82	
100.22/70.82	nubNub' [] wu = nubNub'3 [] wu;
100.22/70.82	nubNub' (x : xs) ls = nubNub'2 (x : xs) ls;
100.22/70.82	
100.22/70.82	nubNub'0 x xs ls True = x : nubNub' xs (x : ls);
100.22/70.82	
100.22/70.82	nubNub'1 x xs ls True = nubNub' xs ls;
100.22/70.82	nubNub'1 x xs ls False = nubNub'0 x xs ls otherwise;
100.22/70.82	
100.22/70.82	nubNub'2 (x : xs) ls = nubNub'1 x xs ls (x `elem` ls);
100.22/70.82	
100.22/70.82	nubNub'3 [] wu = [];
100.22/70.82	nubNub'3 wx wy = nubNub'2 wx wy;
100.22/70.82	
100.22/70.82	}
100.22/70.82	module Main where {
100.22/70.82	import qualified List;
100.22/70.82	import qualified Maybe;
100.22/70.82	import qualified Prelude;
100.22/70.82	}
100.50/70.86	EOF