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 XS)
0.00/0.01	(STRATEGY CONTEXTSENSITIVE
0.00/0.01	(head 1)
0.00/0.01	(incr 1)
0.00/0.01	(nats)
0.00/0.01	(odds)
0.00/0.01	(pairs)
0.00/0.01	(tail 1)
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	head(cons(X,XS)) -> X
0.00/0.01	incr(cons(X,XS)) -> cons(s(X),incr(XS))
0.00/0.01	nats -> cons(0,incr(nats))
0.00/0.01	odds -> incr(pairs)
0.00/0.01	pairs -> cons(0,incr(odds))
0.00/0.01	tail(cons(X,XS)) -> 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	 head(cons(X,XS)) -> X
0.00/0.01	 incr(cons(X,XS)) -> cons(s(X),incr(XS))
0.00/0.01	 nats -> cons(0,incr(nats))
0.00/0.01	 odds -> incr(pairs)
0.00/0.01	 pairs -> cons(0,incr(odds))
0.00/0.01	 tail(cons(X,XS)) -> 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	 ODDS -> INCR(pairs)
0.00/0.01	 ODDS -> PAIRS
0.00/0.01	 TAIL(cons(X,XS)) -> XS
0.00/0.01	-> Rules:
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 incr(cons(X,XS)) -> cons(s(X),incr(XS))
0.00/0.01	 nats -> cons(0,incr(nats))
0.00/0.01	 odds -> incr(pairs)
0.00/0.01	 pairs -> cons(0,incr(odds))
0.00/0.01	 tail(cons(X,XS)) -> XS
0.00/0.01	-> Unhiding Rules:
0.00/0.01	 incr(nats) -> INCR(nats)
0.00/0.01	 incr(nats) -> NATS
0.00/0.01	 incr(odds) -> INCR(odds)
0.00/0.01	 incr(odds) -> ODDS
0.00/0.01	 incr(XS) -> INCR(XS)
0.00/0.01	 incr(x2) -> x2
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	 ODDS -> INCR(pairs)
0.00/0.01	 ODDS -> PAIRS
0.00/0.01	 TAIL(cons(X,XS)) -> XS
0.00/0.01	-> Rules:
0.00/0.01	 head(cons(X,XS)) -> X
0.00/0.01	 incr(cons(X,XS)) -> cons(s(X),incr(XS))
0.00/0.01	 nats -> cons(0,incr(nats))
0.00/0.01	 odds -> incr(pairs)
0.00/0.01	 pairs -> cons(0,incr(odds))
0.00/0.01	 tail(cons(X,XS)) -> XS
0.00/0.01	-> Unhiding rules:
0.00/0.01	 incr(nats) -> INCR(nats)
0.00/0.01	 incr(nats) -> NATS
0.00/0.01	 incr(odds) -> INCR(odds)
0.00/0.01	 incr(odds) -> ODDS
0.00/0.01	 incr(XS) -> INCR(XS)
0.00/0.01	 incr(x2) -> x2
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