0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR X Y)
0.00/0.01	(STRATEGY CONTEXTSENSITIVE
0.00/0.01	(adx 1)
0.00/0.01	(hd 1)
0.00/0.01	(incr 1)
0.00/0.01	(nats)
0.00/0.01	(tl 1)
0.00/0.01	(zeros)
0.00/0.01	(0)
0.00/0.01	(cons)
0.00/0.01	(s)
0.00/0.01	)
0.00/0.01	(RULES
0.00/0.01	adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
0.00/0.01	hd(cons(X,Y)) -> X
0.00/0.01	incr(cons(X,Y)) -> cons(s(X),incr(Y))
0.00/0.01	nats -> adx(zeros)
0.00/0.01	tl(cons(X,Y)) -> Y
0.00/0.01	zeros -> cons(0,zeros)
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	 adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
0.00/0.01	 hd(cons(X,Y)) -> X
0.00/0.01	 incr(cons(X,Y)) -> cons(s(X),incr(Y))
0.00/0.01	 nats -> adx(zeros)
0.00/0.01	 tl(cons(X,Y)) -> Y
0.00/0.01	 zeros -> cons(0,zeros)
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	 ADX(cons(X,Y)) -> INCR(cons(X,adx(Y)))
0.00/0.01	 HD(cons(X,Y)) -> X
0.00/0.01	 NATS -> ADX(zeros)
0.00/0.01	 NATS -> ZEROS
0.00/0.01	 TL(cons(X,Y)) -> Y
0.00/0.01	-> Rules:
0.00/0.01	 adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
0.00/0.01	 hd(cons(X,Y)) -> X
0.00/0.01	 incr(cons(X,Y)) -> cons(s(X),incr(Y))
0.00/0.01	 nats -> adx(zeros)
0.00/0.01	 tl(cons(X,Y)) -> Y
0.00/0.01	 zeros -> cons(0,zeros)
0.00/0.01	-> Unhiding Rules:
0.00/0.01	 adx(Y) -> ADX(Y)
0.00/0.01	 adx(x2) -> x2
0.00/0.01	 incr(Y) -> INCR(Y)
0.00/0.01	 incr(x2) -> x2
0.00/0.01	 zeros -> ZEROS
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	 ADX(cons(X,Y)) -> INCR(cons(X,adx(Y)))
0.00/0.01	 HD(cons(X,Y)) -> X
0.00/0.01	 NATS -> ADX(zeros)
0.00/0.01	 NATS -> ZEROS
0.00/0.01	 TL(cons(X,Y)) -> Y
0.00/0.01	-> Rules:
0.00/0.01	 adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
0.00/0.01	 hd(cons(X,Y)) -> X
0.00/0.01	 incr(cons(X,Y)) -> cons(s(X),incr(Y))
0.00/0.01	 nats -> adx(zeros)
0.00/0.01	 tl(cons(X,Y)) -> Y
0.00/0.01	 zeros -> cons(0,zeros)
0.00/0.01	-> Unhiding rules:
0.00/0.01	 adx(Y) -> ADX(Y)
0.00/0.01	 adx(x2) -> x2
0.00/0.01	 incr(Y) -> INCR(Y)
0.00/0.01	 incr(x2) -> x2
0.00/0.01	 zeros -> ZEROS
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	EOF