0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR N X XS)
0.00/0.01	(STRATEGY CONTEXTSENSITIVE
0.00/0.01	(2nd 1)
0.00/0.01	(from 1)
0.00/0.01	(head 1)
0.00/0.01	(sel 1 2)
0.00/0.01	(take 1 2)
0.00/0.01	(0)
0.00/0.01	(cons 1)
0.00/0.01	(nil)
0.00/0.01	(s 1)
0.00/0.01	)
0.00/0.01	(RULES
0.00/0.01	2nd(cons(X,XS)) -> head(XS)
0.00/0.01	from(X) -> cons(X,from(s(X)))
0.00/0.01	head(cons(X,XS)) -> X
0.00/0.01	sel(0,cons(X,XS)) -> X
0.00/0.01	sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	take(0,XS) -> nil
0.00/0.01	take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	)
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Innermost Equivalent Processor:
0.00/0.01	-> Rules:
0.00/0.01	 2nd(cons(X,XS)) -> head(XS)
0.00/0.01	 from(X) -> cons(X,from(s(X)))
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 sel(0,cons(X,XS)) -> X
0.00/0.01	 sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	 take(0,XS) -> nil
0.00/0.01	 take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
0.00/0.01	 
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Dependency Pairs Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 2ND(cons(X,XS)) -> HEAD(XS)
0.00/0.01	 2ND(cons(X,XS)) -> XS
0.00/0.01	 SEL(s(N),cons(X,XS)) -> SEL(N,XS)
0.00/0.01	 SEL(s(N),cons(X,XS)) -> XS
0.00/0.01	-> Rules:
0.00/0.01	 2nd(cons(X,XS)) -> head(XS)
0.00/0.01	 from(X) -> cons(X,from(s(X)))
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 sel(0,cons(X,XS)) -> X
0.00/0.01	 sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	 take(0,XS) -> nil
0.00/0.01	 take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	-> Unhiding Rules:
0.00/0.01	 from(s(X)) -> FROM(s(X))
0.00/0.01	 take(N,XS) -> TAKE(N,XS)
0.00/0.01	 take(N,x3) -> x3
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 2ND(cons(X,XS)) -> HEAD(XS)
0.00/0.01	 2ND(cons(X,XS)) -> XS
0.00/0.01	 SEL(s(N),cons(X,XS)) -> SEL(N,XS)
0.00/0.01	 SEL(s(N),cons(X,XS)) -> XS
0.00/0.01	-> Rules:
0.00/0.01	 2nd(cons(X,XS)) -> head(XS)
0.00/0.01	 from(X) -> cons(X,from(s(X)))
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 sel(0,cons(X,XS)) -> X
0.00/0.01	 sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	 take(0,XS) -> nil
0.00/0.01	 take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	-> Unhiding rules:
0.00/0.01	 from(s(X)) -> FROM(s(X))
0.00/0.01	 take(N,XS) -> TAKE(N,XS)
0.00/0.01	 take(N,x3) -> x3
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 SEL(s(N),cons(X,XS)) -> SEL(N,XS)
0.00/0.01	->->-> Rules:
0.00/0.01	 2nd(cons(X,XS)) -> head(XS)
0.00/0.01	 from(X) -> cons(X,from(s(X)))
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 sel(0,cons(X,XS)) -> X
0.00/0.01	 sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	 take(0,XS) -> nil
0.00/0.01	 take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	->->-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	SubNColl Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 SEL(s(N),cons(X,XS)) -> SEL(N,XS)
0.00/0.01	-> Rules:
0.00/0.01	 2nd(cons(X,XS)) -> head(XS)
0.00/0.01	 from(X) -> cons(X,from(s(X)))
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 sel(0,cons(X,XS)) -> X
0.00/0.01	 sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	 take(0,XS) -> nil
0.00/0.01	 take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->Projection:
0.00/0.01	 pi(SEL) = 1
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Basic Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 2nd(cons(X,XS)) -> head(XS)
0.00/0.01	 from(X) -> cons(X,from(s(X)))
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 sel(0,cons(X,XS)) -> X
0.00/0.01	 sel(s(N),cons(X,XS)) -> sel(N,XS)
0.00/0.01	 take(0,XS) -> nil
0.00/0.01	 take(s(N),cons(X,XS)) -> cons(X,take(N,XS))
0.00/0.01	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	-> Result:
0.00/0.01	 Set P is empty
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	EOF