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 Y)
0.00/0.01	(STRATEGY CONTEXTSENSITIVE
0.00/0.01	(add 1 2)
0.00/0.01	(fib 1)
0.00/0.01	(fib1 1 2)
0.00/0.01	(sel 1 2)
0.00/0.01	(0)
0.00/0.01	(cons 1)
0.00/0.01	(s 1)
0.00/0.01	)
0.00/0.01	(RULES
0.00/0.01	add(0,X) -> X
0.00/0.01	add(s(X),Y) -> s(add(X,Y))
0.00/0.01	fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	)
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> 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	 ADD(s(X),Y) -> ADD(X,Y)
0.00/0.01	 FIB(N) -> FIB1(s(0),s(0))
0.00/0.01	 FIB(N) -> SEL(N,fib1(s(0),s(0)))
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> Unhiding Rules:
0.00/0.01	 fib1(Y,add(X,Y)) -> ADD(X,Y)
0.00/0.01	 fib1(Y,add(X,Y)) -> FIB1(Y,add(X,Y))
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	 ADD(s(X),Y) -> ADD(X,Y)
0.00/0.01	 FIB(N) -> FIB1(s(0),s(0))
0.00/0.01	 FIB(N) -> SEL(N,fib1(s(0),s(0)))
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> Unhiding rules:
0.00/0.01	 fib1(Y,add(X,Y)) -> ADD(X,Y)
0.00/0.01	 fib1(Y,add(X,Y)) -> FIB1(Y,add(X,Y))
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 ADD(s(X),Y) -> ADD(X,Y)
0.00/0.01	->->-> Rules:
0.00/0.01	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	->->-> Unhiding rules:
0.00/0.01	 Empty
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	->->-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	
0.00/0.01	
0.00/0.01	The problem is decomposed in 2 subproblems.
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SubNColl Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 ADD(s(X),Y) -> ADD(X,Y)
0.00/0.01	-> Rules:
0.00/0.01	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->Projection:
0.00/0.01	 pi(ADD) = 1
0.00/0.01	
0.00/0.01	Problem 1.1: 
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> 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	
0.00/0.01	Problem 1.2: 
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> 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 1.2: 
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	 add(0,X) -> X
0.00/0.01	 add(s(X),Y) -> s(add(X,Y))
0.00/0.01	 fib(N) -> sel(N,fib1(s(0),s(0)))
0.00/0.01	 fib1(X,Y) -> cons(X,fib1(Y,add(X,Y)))
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	-> 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