0.00/0.03	YES
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	(VAR X Y)
0.00/0.03	(STRATEGY CONTEXTSENSITIVE
0.00/0.03	(from 1)
0.00/0.03	(length)
0.00/0.03	(length1)
0.00/0.03	(0)
0.00/0.03	(cons 1)
0.00/0.03	(nil)
0.00/0.03	(s 1)
0.00/0.03	)
0.00/0.03	(RULES
0.00/0.03	from(X) -> cons(X,from(s(X)))
0.00/0.03	length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	length(nil) -> 0
0.00/0.03	length1(X) -> length(X)
0.00/0.03	)
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Innermost Equivalent Processor:
0.00/0.03	-> Rules:
0.00/0.03	 from(X) -> cons(X,from(s(X)))
0.00/0.03	 length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	 length(nil) -> 0
0.00/0.03	 length1(X) -> length(X)
0.00/0.03	-> The context-sensitive term rewriting system is an orthogonal system. Therefore, innermost cs-termination implies cs-termination.
0.00/0.03	 
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Dependency Pairs Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 LENGTH(cons(X,Y)) -> LENGTH1(Y)
0.00/0.03	 LENGTH1(X) -> LENGTH(X)
0.00/0.03	-> Rules:
0.00/0.03	 from(X) -> cons(X,from(s(X)))
0.00/0.03	 length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	 length(nil) -> 0
0.00/0.03	 length1(X) -> length(X)
0.00/0.03	-> Unhiding Rules:
0.00/0.03	 Empty
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 LENGTH(cons(X,Y)) -> LENGTH1(Y)
0.00/0.03	 LENGTH1(X) -> LENGTH(X)
0.00/0.03	-> Rules:
0.00/0.03	 from(X) -> cons(X,from(s(X)))
0.00/0.03	 length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	 length(nil) -> 0
0.00/0.03	 length1(X) -> length(X)
0.00/0.03	-> Unhiding rules:
0.00/0.03	 Empty
0.00/0.03	->Strongly Connected Components:
0.00/0.03	->->Cycle:
0.00/0.03	->->-> Pairs:
0.00/0.03	 LENGTH(cons(X,Y)) -> LENGTH1(Y)
0.00/0.03	 LENGTH1(X) -> LENGTH(X)
0.00/0.03	->->-> Rules:
0.00/0.03	 from(X) -> cons(X,from(s(X)))
0.00/0.03	 length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	 length(nil) -> 0
0.00/0.03	 length1(X) -> length(X)
0.00/0.03	->->-> Unhiding rules:
0.00/0.03	 Empty
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	Reduction Pairs Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 LENGTH(cons(X,Y)) -> LENGTH1(Y)
0.00/0.03	 LENGTH1(X) -> LENGTH(X)
0.00/0.03	-> Rules:
0.00/0.03	 from(X) -> cons(X,from(s(X)))
0.00/0.03	 length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	 length(nil) -> 0
0.00/0.03	 length1(X) -> length(X)
0.00/0.03	-> Unhiding rules:
0.00/0.03	 Empty
0.00/0.03	-> Usable rules:
0.00/0.03	 Empty
0.00/0.03	->Interpretation type:
0.00/0.03	 Linear
0.00/0.03	->Coefficients:
0.00/0.03	 Natural Numbers
0.00/0.03	->Dimension:
0.00/0.03	 1
0.00/0.03	->Bound:
0.00/0.03	 2
0.00/0.03	->Interpretation:
0.00/0.03	 
0.00/0.03	[cons](X1,X2) = 2.X2 + 2
0.00/0.03	[LENGTH](X) = 2.X + 2
0.00/0.03	[LENGTH1](X) = 2.X + 2
0.00/0.03	
0.00/0.03	Problem 1: 
0.00/0.03	
0.00/0.03	SCC Processor:
0.00/0.03	-> Pairs:
0.00/0.03	 LENGTH1(X) -> LENGTH(X)
0.00/0.03	-> Rules:
0.00/0.03	 from(X) -> cons(X,from(s(X)))
0.00/0.03	 length(cons(X,Y)) -> s(length1(Y))
0.00/0.03	 length(nil) -> 0
0.00/0.03	 length1(X) -> length(X)
0.00/0.03	-> Unhiding rules:
0.00/0.03	 Empty
0.00/0.03	->Strongly Connected Components:
0.00/0.03	 There is no strongly connected component
0.00/0.03	
0.00/0.03	The problem is finite.
0.00/0.03	EOF