0.00/0.04	YES
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	(VAR L X Y)
0.00/0.04	(STRATEGY CONTEXTSENSITIVE
0.00/0.04	(eq)
0.00/0.04	(inf 1)
0.00/0.04	(length 1)
0.00/0.04	(take 1 2)
0.00/0.04	(0)
0.00/0.04	(cons)
0.00/0.04	(false)
0.00/0.04	(nil)
0.00/0.04	(s)
0.00/0.04	(true)
0.00/0.04	)
0.00/0.04	(RULES
0.00/0.04	eq(0,0) -> true
0.00/0.04	eq(s(X),s(Y)) -> eq(X,Y)
0.00/0.04	eq(X,Y) -> false
0.00/0.04	inf(X) -> cons(X,inf(s(X)))
0.00/0.04	length(cons(X,L)) -> s(length(L))
0.00/0.04	length(nil) -> 0
0.00/0.04	take(0,X) -> nil
0.00/0.04	take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
0.00/0.04	)
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	Dependency Pairs Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 EQ(s(X),s(Y)) -> EQ(X,Y)
0.00/0.04	-> Rules:
0.00/0.04	 eq(0,0) -> true
0.00/0.04	 eq(s(X),s(Y)) -> eq(X,Y)
0.00/0.04	 eq(X,Y) -> false
0.00/0.04	 inf(X) -> cons(X,inf(s(X)))
0.00/0.04	 length(cons(X,L)) -> s(length(L))
0.00/0.04	 length(nil) -> 0
0.00/0.04	 take(0,X) -> nil
0.00/0.04	 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
0.00/0.04	-> Unhiding Rules:
0.00/0.04	 Empty
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	SCC Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 EQ(s(X),s(Y)) -> EQ(X,Y)
0.00/0.04	-> Rules:
0.00/0.04	 eq(0,0) -> true
0.00/0.04	 eq(s(X),s(Y)) -> eq(X,Y)
0.00/0.04	 eq(X,Y) -> false
0.00/0.04	 inf(X) -> cons(X,inf(s(X)))
0.00/0.04	 length(cons(X,L)) -> s(length(L))
0.00/0.04	 length(nil) -> 0
0.00/0.04	 take(0,X) -> nil
0.00/0.04	 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
0.00/0.04	-> Unhiding rules:
0.00/0.04	 Empty
0.00/0.04	->Strongly Connected Components:
0.00/0.04	->->Cycle:
0.00/0.04	->->-> Pairs:
0.00/0.04	 EQ(s(X),s(Y)) -> EQ(X,Y)
0.00/0.04	->->-> Rules:
0.00/0.04	 eq(0,0) -> true
0.00/0.04	 eq(s(X),s(Y)) -> eq(X,Y)
0.00/0.04	 eq(X,Y) -> false
0.00/0.04	 inf(X) -> cons(X,inf(s(X)))
0.00/0.04	 length(cons(X,L)) -> s(length(L))
0.00/0.04	 length(nil) -> 0
0.00/0.04	 take(0,X) -> nil
0.00/0.04	 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
0.00/0.04	->->-> Unhiding rules:
0.00/0.04	 Empty
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	Reduction Pairs Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 EQ(s(X),s(Y)) -> EQ(X,Y)
0.00/0.04	-> Rules:
0.00/0.04	 eq(0,0) -> true
0.00/0.04	 eq(s(X),s(Y)) -> eq(X,Y)
0.00/0.04	 eq(X,Y) -> false
0.00/0.04	 inf(X) -> cons(X,inf(s(X)))
0.00/0.04	 length(cons(X,L)) -> s(length(L))
0.00/0.04	 length(nil) -> 0
0.00/0.04	 take(0,X) -> nil
0.00/0.04	 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
0.00/0.04	-> Unhiding rules:
0.00/0.04	 Empty
0.00/0.04	-> Usable rules:
0.00/0.04	 Empty
0.00/0.04	->Interpretation type:
0.00/0.04	 Linear
0.00/0.04	->Coefficients:
0.00/0.04	 Natural Numbers
0.00/0.04	->Dimension:
0.00/0.04	 1
0.00/0.04	->Bound:
0.00/0.04	 2
0.00/0.04	->Interpretation:
0.00/0.04	 
0.00/0.04	[s](X) = 2.X + 2
0.00/0.04	[EQ](X1,X2) = 2.X1 + 2.X2
0.00/0.04	
0.00/0.04	Problem 1: 
0.00/0.04	
0.00/0.04	Basic Processor:
0.00/0.04	-> Pairs:
0.00/0.04	 Empty
0.00/0.04	-> Rules:
0.00/0.04	 eq(0,0) -> true
0.00/0.04	 eq(s(X),s(Y)) -> eq(X,Y)
0.00/0.04	 eq(X,Y) -> false
0.00/0.04	 inf(X) -> cons(X,inf(s(X)))
0.00/0.04	 length(cons(X,L)) -> s(length(L))
0.00/0.04	 length(nil) -> 0
0.00/0.04	 take(0,X) -> nil
0.00/0.04	 take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
0.00/0.04	-> Unhiding rules:
0.00/0.04	 Empty
0.00/0.04	-> Result:
0.00/0.04	 Set P is empty
0.00/0.04	
0.00/0.04	The problem is finite.
0.00/0.05	EOF