3.61/4.39	YES
3.61/4.39	
3.61/4.39	Problem 1: 
3.61/4.39	
3.61/4.39	(VAR v_NonEmpty:S L:S X:S X1:S X2:S)
3.61/4.39	(RULES
3.61/4.39	active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	active(adx(nil)) -> mark(nil)
3.61/4.39	active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	active(incr(nil)) -> mark(nil)
3.61/4.39	active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	active(nats) -> mark(adx(zeros))
3.61/4.39	active(zeros) -> mark(cons(0,zeros))
3.61/4.39	adx(active(X:S)) -> adx(X:S)
3.61/4.39	adx(mark(X:S)) -> adx(X:S)
3.61/4.39	cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	head(active(X:S)) -> head(X:S)
3.61/4.39	head(mark(X:S)) -> head(X:S)
3.61/4.39	incr(active(X:S)) -> incr(X:S)
3.61/4.39	incr(mark(X:S)) -> incr(X:S)
3.61/4.39	mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	mark(0) -> active(0)
3.61/4.39	mark(nats) -> active(nats)
3.61/4.39	mark(nil) -> active(nil)
3.61/4.39	mark(zeros) -> active(zeros)
3.61/4.39	s(active(X:S)) -> s(X:S)
3.61/4.39	s(mark(X:S)) -> s(X:S)
3.61/4.39	tail(active(X:S)) -> tail(X:S)
3.61/4.39	tail(mark(X:S)) -> tail(X:S)
3.61/4.39	) 
3.61/4.39	(STRATEGY INNERMOST)
3.61/4.39	
3.61/4.39	Problem 1: 
3.61/4.39	
3.61/4.39	Dependency Pairs Processor:
3.61/4.39	-> Pairs:
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> ADX(L:S)
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> CONS(X:S,adx(L:S))
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> INCR(cons(X:S,adx(L:S)))
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.39	 ACTIVE(adx(nil)) -> MARK(nil)
3.61/4.39	 ACTIVE(head(cons(X:S,L:S))) -> MARK(X:S)
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> CONS(s(X:S),incr(L:S))
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> INCR(L:S)
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> S(X:S)
3.61/4.39	 ACTIVE(incr(nil)) -> MARK(nil)
3.61/4.39	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.39	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.39	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.39	 ADX(active(X:S)) -> ADX(X:S)
3.61/4.39	 ADX(mark(X:S)) -> ADX(X:S)
3.61/4.39	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.39	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.39	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.39	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.39	 HEAD(active(X:S)) -> HEAD(X:S)
3.61/4.39	 HEAD(mark(X:S)) -> HEAD(X:S)
3.61/4.39	 INCR(active(X:S)) -> INCR(X:S)
3.61/4.39	 INCR(mark(X:S)) -> INCR(X:S)
3.61/4.39	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.39	 MARK(adx(X:S)) -> ADX(mark(X:S))
3.61/4.39	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.39	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
3.61/4.39	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.39	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.39	 MARK(head(X:S)) -> HEAD(mark(X:S))
3.61/4.39	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.39	 MARK(incr(X:S)) -> INCR(mark(X:S))
3.61/4.39	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.39	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(s(X:S)) -> S(mark(X:S))
3.61/4.39	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.39	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(tail(X:S)) -> TAIL(mark(X:S))
3.61/4.39	 MARK(nats) -> ACTIVE(nats)
3.61/4.39	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.39	 S(active(X:S)) -> S(X:S)
3.61/4.39	 S(mark(X:S)) -> S(X:S)
3.61/4.39	 TAIL(active(X:S)) -> TAIL(X:S)
3.61/4.39	 TAIL(mark(X:S)) -> TAIL(X:S)
3.61/4.39	-> Rules:
3.61/4.39	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	 active(adx(nil)) -> mark(nil)
3.61/4.39	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	 active(incr(nil)) -> mark(nil)
3.61/4.39	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	 active(nats) -> mark(adx(zeros))
3.61/4.39	 active(zeros) -> mark(cons(0,zeros))
3.61/4.39	 adx(active(X:S)) -> adx(X:S)
3.61/4.39	 adx(mark(X:S)) -> adx(X:S)
3.61/4.39	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 head(active(X:S)) -> head(X:S)
3.61/4.39	 head(mark(X:S)) -> head(X:S)
3.61/4.39	 incr(active(X:S)) -> incr(X:S)
3.61/4.39	 incr(mark(X:S)) -> incr(X:S)
3.61/4.39	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	 mark(0) -> active(0)
3.61/4.39	 mark(nats) -> active(nats)
3.61/4.39	 mark(nil) -> active(nil)
3.61/4.39	 mark(zeros) -> active(zeros)
3.61/4.39	 s(active(X:S)) -> s(X:S)
3.61/4.39	 s(mark(X:S)) -> s(X:S)
3.61/4.39	 tail(active(X:S)) -> tail(X:S)
3.61/4.39	 tail(mark(X:S)) -> tail(X:S)
3.61/4.39	
3.61/4.39	Problem 1: 
3.61/4.39	
3.61/4.39	SCC Processor:
3.61/4.39	-> Pairs:
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> ADX(L:S)
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> CONS(X:S,adx(L:S))
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> INCR(cons(X:S,adx(L:S)))
3.61/4.39	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.39	 ACTIVE(adx(nil)) -> MARK(nil)
3.61/4.39	 ACTIVE(head(cons(X:S,L:S))) -> MARK(X:S)
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> CONS(s(X:S),incr(L:S))
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> INCR(L:S)
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.39	 ACTIVE(incr(cons(X:S,L:S))) -> S(X:S)
3.61/4.39	 ACTIVE(incr(nil)) -> MARK(nil)
3.61/4.39	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.39	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.39	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.39	 ADX(active(X:S)) -> ADX(X:S)
3.61/4.39	 ADX(mark(X:S)) -> ADX(X:S)
3.61/4.39	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.39	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.39	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.39	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.39	 HEAD(active(X:S)) -> HEAD(X:S)
3.61/4.39	 HEAD(mark(X:S)) -> HEAD(X:S)
3.61/4.39	 INCR(active(X:S)) -> INCR(X:S)
3.61/4.39	 INCR(mark(X:S)) -> INCR(X:S)
3.61/4.39	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.39	 MARK(adx(X:S)) -> ADX(mark(X:S))
3.61/4.39	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.39	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
3.61/4.39	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.39	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.39	 MARK(head(X:S)) -> HEAD(mark(X:S))
3.61/4.39	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.39	 MARK(incr(X:S)) -> INCR(mark(X:S))
3.61/4.39	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.39	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(s(X:S)) -> S(mark(X:S))
3.61/4.39	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.39	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.39	 MARK(tail(X:S)) -> TAIL(mark(X:S))
3.61/4.39	 MARK(nats) -> ACTIVE(nats)
3.61/4.39	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.39	 S(active(X:S)) -> S(X:S)
3.61/4.39	 S(mark(X:S)) -> S(X:S)
3.61/4.39	 TAIL(active(X:S)) -> TAIL(X:S)
3.61/4.39	 TAIL(mark(X:S)) -> TAIL(X:S)
3.61/4.39	-> Rules:
3.61/4.39	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	 active(adx(nil)) -> mark(nil)
3.61/4.39	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	 active(incr(nil)) -> mark(nil)
3.61/4.39	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	 active(nats) -> mark(adx(zeros))
3.61/4.39	 active(zeros) -> mark(cons(0,zeros))
3.61/4.39	 adx(active(X:S)) -> adx(X:S)
3.61/4.39	 adx(mark(X:S)) -> adx(X:S)
3.61/4.39	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 head(active(X:S)) -> head(X:S)
3.61/4.39	 head(mark(X:S)) -> head(X:S)
3.61/4.39	 incr(active(X:S)) -> incr(X:S)
3.61/4.39	 incr(mark(X:S)) -> incr(X:S)
3.61/4.39	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	 mark(0) -> active(0)
3.61/4.39	 mark(nats) -> active(nats)
3.61/4.39	 mark(nil) -> active(nil)
3.61/4.39	 mark(zeros) -> active(zeros)
3.61/4.39	 s(active(X:S)) -> s(X:S)
3.61/4.39	 s(mark(X:S)) -> s(X:S)
3.61/4.39	 tail(active(X:S)) -> tail(X:S)
3.61/4.39	 tail(mark(X:S)) -> tail(X:S)
3.61/4.39	->Strongly Connected Components:
3.61/4.39	->->Cycle:
3.61/4.39	->->-> Pairs:
3.61/4.39	 TAIL(active(X:S)) -> TAIL(X:S)
3.61/4.39	 TAIL(mark(X:S)) -> TAIL(X:S)
3.61/4.39	->->-> Rules:
3.61/4.39	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	 active(adx(nil)) -> mark(nil)
3.61/4.39	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	 active(incr(nil)) -> mark(nil)
3.61/4.39	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	 active(nats) -> mark(adx(zeros))
3.61/4.39	 active(zeros) -> mark(cons(0,zeros))
3.61/4.39	 adx(active(X:S)) -> adx(X:S)
3.61/4.39	 adx(mark(X:S)) -> adx(X:S)
3.61/4.39	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 head(active(X:S)) -> head(X:S)
3.61/4.39	 head(mark(X:S)) -> head(X:S)
3.61/4.39	 incr(active(X:S)) -> incr(X:S)
3.61/4.39	 incr(mark(X:S)) -> incr(X:S)
3.61/4.39	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	 mark(0) -> active(0)
3.61/4.39	 mark(nats) -> active(nats)
3.61/4.39	 mark(nil) -> active(nil)
3.61/4.39	 mark(zeros) -> active(zeros)
3.61/4.39	 s(active(X:S)) -> s(X:S)
3.61/4.39	 s(mark(X:S)) -> s(X:S)
3.61/4.39	 tail(active(X:S)) -> tail(X:S)
3.61/4.39	 tail(mark(X:S)) -> tail(X:S)
3.61/4.39	->->Cycle:
3.61/4.39	->->-> Pairs:
3.61/4.39	 S(active(X:S)) -> S(X:S)
3.61/4.39	 S(mark(X:S)) -> S(X:S)
3.61/4.39	->->-> Rules:
3.61/4.39	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	 active(adx(nil)) -> mark(nil)
3.61/4.39	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	 active(incr(nil)) -> mark(nil)
3.61/4.39	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	 active(nats) -> mark(adx(zeros))
3.61/4.39	 active(zeros) -> mark(cons(0,zeros))
3.61/4.39	 adx(active(X:S)) -> adx(X:S)
3.61/4.39	 adx(mark(X:S)) -> adx(X:S)
3.61/4.39	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 head(active(X:S)) -> head(X:S)
3.61/4.39	 head(mark(X:S)) -> head(X:S)
3.61/4.39	 incr(active(X:S)) -> incr(X:S)
3.61/4.39	 incr(mark(X:S)) -> incr(X:S)
3.61/4.39	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	 mark(0) -> active(0)
3.61/4.39	 mark(nats) -> active(nats)
3.61/4.39	 mark(nil) -> active(nil)
3.61/4.39	 mark(zeros) -> active(zeros)
3.61/4.39	 s(active(X:S)) -> s(X:S)
3.61/4.39	 s(mark(X:S)) -> s(X:S)
3.61/4.39	 tail(active(X:S)) -> tail(X:S)
3.61/4.39	 tail(mark(X:S)) -> tail(X:S)
3.61/4.39	->->Cycle:
3.61/4.39	->->-> Pairs:
3.61/4.39	 INCR(active(X:S)) -> INCR(X:S)
3.61/4.39	 INCR(mark(X:S)) -> INCR(X:S)
3.61/4.39	->->-> Rules:
3.61/4.39	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	 active(adx(nil)) -> mark(nil)
3.61/4.39	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	 active(incr(nil)) -> mark(nil)
3.61/4.39	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	 active(nats) -> mark(adx(zeros))
3.61/4.39	 active(zeros) -> mark(cons(0,zeros))
3.61/4.39	 adx(active(X:S)) -> adx(X:S)
3.61/4.39	 adx(mark(X:S)) -> adx(X:S)
3.61/4.39	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 head(active(X:S)) -> head(X:S)
3.61/4.39	 head(mark(X:S)) -> head(X:S)
3.61/4.39	 incr(active(X:S)) -> incr(X:S)
3.61/4.39	 incr(mark(X:S)) -> incr(X:S)
3.61/4.39	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	 mark(0) -> active(0)
3.61/4.39	 mark(nats) -> active(nats)
3.61/4.39	 mark(nil) -> active(nil)
3.61/4.39	 mark(zeros) -> active(zeros)
3.61/4.39	 s(active(X:S)) -> s(X:S)
3.61/4.39	 s(mark(X:S)) -> s(X:S)
3.61/4.39	 tail(active(X:S)) -> tail(X:S)
3.61/4.39	 tail(mark(X:S)) -> tail(X:S)
3.61/4.39	->->Cycle:
3.61/4.39	->->-> Pairs:
3.61/4.39	 HEAD(active(X:S)) -> HEAD(X:S)
3.61/4.39	 HEAD(mark(X:S)) -> HEAD(X:S)
3.61/4.39	->->-> Rules:
3.61/4.39	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.39	 active(adx(nil)) -> mark(nil)
3.61/4.39	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.39	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.39	 active(incr(nil)) -> mark(nil)
3.61/4.39	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.39	 active(nats) -> mark(adx(zeros))
3.61/4.39	 active(zeros) -> mark(cons(0,zeros))
3.61/4.39	 adx(active(X:S)) -> adx(X:S)
3.61/4.39	 adx(mark(X:S)) -> adx(X:S)
3.61/4.39	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.39	 head(active(X:S)) -> head(X:S)
3.61/4.39	 head(mark(X:S)) -> head(X:S)
3.61/4.39	 incr(active(X:S)) -> incr(X:S)
3.61/4.39	 incr(mark(X:S)) -> incr(X:S)
3.61/4.39	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.39	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.39	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.39	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.39	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.39	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.39	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ADX(active(X:S)) -> ADX(X:S)
3.61/4.40	 ADX(mark(X:S)) -> ADX(X:S)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(head(cons(X:S,L:S))) -> MARK(X:S)
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	
3.61/4.40	The problem is decomposed in 7 subproblems.
3.61/4.40	
3.61/4.40	Problem 1.1: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 TAIL(active(X:S)) -> TAIL(X:S)
3.61/4.40	 TAIL(mark(X:S)) -> TAIL(X:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(TAIL) = 1
3.61/4.40	
3.61/4.40	Problem 1.1: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 Empty
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	 There is no strongly connected component
3.61/4.40	
3.61/4.40	The problem is finite.
3.61/4.40	
3.61/4.40	Problem 1.2: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 S(active(X:S)) -> S(X:S)
3.61/4.40	 S(mark(X:S)) -> S(X:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(S) = 1
3.61/4.40	
3.61/4.40	Problem 1.2: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 Empty
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	 There is no strongly connected component
3.61/4.40	
3.61/4.40	The problem is finite.
3.61/4.40	
3.61/4.40	Problem 1.3: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 INCR(active(X:S)) -> INCR(X:S)
3.61/4.40	 INCR(mark(X:S)) -> INCR(X:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(INCR) = 1
3.61/4.40	
3.61/4.40	Problem 1.3: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 Empty
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	 There is no strongly connected component
3.61/4.40	
3.61/4.40	The problem is finite.
3.61/4.40	
3.61/4.40	Problem 1.4: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 HEAD(active(X:S)) -> HEAD(X:S)
3.61/4.40	 HEAD(mark(X:S)) -> HEAD(X:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(HEAD) = 1
3.61/4.40	
3.61/4.40	Problem 1.4: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 Empty
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	 There is no strongly connected component
3.61/4.40	
3.61/4.40	The problem is finite.
3.61/4.40	
3.61/4.40	Problem 1.5: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(CONS) = 1
3.61/4.40	
3.61/4.40	Problem 1.5: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	Problem 1.5: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(CONS) = 2
3.61/4.40	
3.61/4.40	Problem 1.5: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 Empty
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	 There is no strongly connected component
3.61/4.40	
3.61/4.40	The problem is finite.
3.61/4.40	
3.61/4.40	Problem 1.6: 
3.61/4.40	
3.61/4.40	Subterm Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ADX(active(X:S)) -> ADX(X:S)
3.61/4.40	 ADX(mark(X:S)) -> ADX(X:S)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Projection:
3.61/4.40	 pi(ADX) = 1
3.61/4.40	
3.61/4.40	Problem 1.6: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 Empty
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	 There is no strongly connected component
3.61/4.40	
3.61/4.40	The problem is finite.
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	Reduction Pairs Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(head(cons(X:S,L:S))) -> MARK(X:S)
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	-> Usable rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Interpretation type:
3.61/4.40	 Linear
3.61/4.40	->Coefficients:
3.61/4.40	 Natural Numbers
3.61/4.40	->Dimension:
3.61/4.40	 1
3.61/4.40	->Bound:
3.61/4.40	 2
3.61/4.40	->Interpretation:
3.61/4.40	 
3.61/4.40	[active](X) = X
3.61/4.40	[adx](X) = 2.X
3.61/4.40	[cons](X1,X2) = 2.X1 + 2.X2
3.61/4.40	[head](X) = 2.X + 2
3.61/4.40	[incr](X) = X
3.61/4.40	[mark](X) = X
3.61/4.40	[s](X) = X
3.61/4.40	[tail](X) = 2.X + 1
3.61/4.40	[0] = 0
3.61/4.40	[fSNonEmpty] = 0
3.61/4.40	[nats] = 2
3.61/4.40	[nil] = 2
3.61/4.40	[zeros] = 0
3.61/4.40	[ACTIVE](X) = 2.X + 1
3.61/4.40	[ADX](X) = 0
3.61/4.40	[CONS](X1,X2) = 0
3.61/4.40	[HEAD](X) = 0
3.61/4.40	[INCR](X) = 0
3.61/4.40	[MARK](X) = 2.X + 1
3.61/4.40	[S](X) = 0
3.61/4.40	[TAIL](X) = 0
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	Reduction Pairs Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(tail(cons(X:S,L:S))) -> MARK(L:S)
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	-> Usable rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Interpretation type:
3.61/4.40	 Linear
3.61/4.40	->Coefficients:
3.61/4.40	 Natural Numbers
3.61/4.40	->Dimension:
3.61/4.40	 1
3.61/4.40	->Bound:
3.61/4.40	 2
3.61/4.40	->Interpretation:
3.61/4.40	 
3.61/4.40	[active](X) = X
3.61/4.40	[adx](X) = 2.X
3.61/4.40	[cons](X1,X2) = 2.X1 + 2.X2
3.61/4.40	[head](X) = 2.X + 2
3.61/4.40	[incr](X) = X
3.61/4.40	[mark](X) = X
3.61/4.40	[s](X) = X
3.61/4.40	[tail](X) = X + 2
3.61/4.40	[0] = 0
3.61/4.40	[fSNonEmpty] = 0
3.61/4.40	[nats] = 2
3.61/4.40	[nil] = 2
3.61/4.40	[zeros] = 0
3.61/4.40	[ACTIVE](X) = 2.X + 2
3.61/4.40	[ADX](X) = 0
3.61/4.40	[CONS](X1,X2) = 0
3.61/4.40	[HEAD](X) = 0
3.61/4.40	[INCR](X) = 0
3.61/4.40	[MARK](X) = 2.X + 2
3.61/4.40	[S](X) = 0
3.61/4.40	[TAIL](X) = 0
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	Reduction Pairs Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(nats) -> MARK(adx(zeros))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	-> Usable rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Interpretation type:
3.61/4.40	 Linear
3.61/4.40	->Coefficients:
3.61/4.40	 Natural Numbers
3.61/4.40	->Dimension:
3.61/4.40	 1
3.61/4.40	->Bound:
3.61/4.40	 2
3.61/4.40	->Interpretation:
3.61/4.40	 
3.61/4.40	[active](X) = X
3.61/4.40	[adx](X) = 2.X
3.61/4.40	[cons](X1,X2) = 2.X1 + 2.X2
3.61/4.40	[head](X) = 2.X + 1
3.61/4.40	[incr](X) = X
3.61/4.40	[mark](X) = X
3.61/4.40	[s](X) = X
3.61/4.40	[tail](X) = X + 1
3.61/4.40	[0] = 0
3.61/4.40	[fSNonEmpty] = 0
3.61/4.40	[nats] = 1
3.61/4.40	[nil] = 2
3.61/4.40	[zeros] = 0
3.61/4.40	[ACTIVE](X) = 2.X + 2
3.61/4.40	[ADX](X) = 0
3.61/4.40	[CONS](X1,X2) = 0
3.61/4.40	[HEAD](X) = 0
3.61/4.40	[INCR](X) = 0
3.61/4.40	[MARK](X) = 2.X + 2
3.61/4.40	[S](X) = 0
3.61/4.40	[TAIL](X) = 0
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(nats) -> ACTIVE(nats)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	Reduction Pairs Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(adx(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	-> Usable rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Interpretation type:
3.61/4.40	 Linear
3.61/4.40	->Coefficients:
3.61/4.40	 Natural Numbers
3.61/4.40	->Dimension:
3.61/4.40	 1
3.61/4.40	->Bound:
3.61/4.40	 2
3.61/4.40	->Interpretation:
3.61/4.40	 
3.61/4.40	[active](X) = X
3.61/4.40	[adx](X) = X + 2
3.61/4.40	[cons](X1,X2) = 2.X1 + X2
3.61/4.40	[head](X) = 2.X + 2
3.61/4.40	[incr](X) = X
3.61/4.40	[mark](X) = X
3.61/4.40	[s](X) = X
3.61/4.40	[tail](X) = 2.X + 2
3.61/4.40	[0] = 0
3.61/4.40	[fSNonEmpty] = 0
3.61/4.40	[nats] = 2
3.61/4.40	[nil] = 2
3.61/4.40	[zeros] = 0
3.61/4.40	[ACTIVE](X) = 2.X + 2
3.61/4.40	[ADX](X) = 0
3.61/4.40	[CONS](X1,X2) = 0
3.61/4.40	[HEAD](X) = 0
3.61/4.40	[INCR](X) = 0
3.61/4.40	[MARK](X) = 2.X + 2
3.61/4.40	[S](X) = 0
3.61/4.40	[TAIL](X) = 0
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	Reduction Pairs Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	-> Usable rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Interpretation type:
3.61/4.40	 Linear
3.61/4.40	->Coefficients:
3.61/4.40	 Natural Numbers
3.61/4.40	->Dimension:
3.61/4.40	 1
3.61/4.40	->Bound:
3.61/4.40	 2
3.61/4.40	->Interpretation:
3.61/4.40	 
3.61/4.40	[active](X) = 1
3.61/4.40	[adx](X) = 2
3.61/4.40	[cons](X1,X2) = 0
3.61/4.40	[head](X) = 2
3.61/4.40	[incr](X) = 2
3.61/4.40	[mark](X) = 1
3.61/4.40	[s](X) = 0
3.61/4.40	[tail](X) = 0
3.61/4.40	[0] = 0
3.61/4.40	[fSNonEmpty] = 0
3.61/4.40	[nats] = 0
3.61/4.40	[nil] = 2
3.61/4.40	[zeros] = 2
3.61/4.40	[ACTIVE](X) = X
3.61/4.40	[ADX](X) = 0
3.61/4.40	[CONS](X1,X2) = 0
3.61/4.40	[HEAD](X) = 0
3.61/4.40	[INCR](X) = 0
3.61/4.40	[MARK](X) = 2
3.61/4.40	[S](X) = 0
3.61/4.40	[TAIL](X) = 0
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Strongly Connected Components:
3.61/4.40	->->Cycle:
3.61/4.40	->->-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	->->-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	Reduction Pairs Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.40	 MARK(head(X:S)) -> ACTIVE(head(mark(X:S)))
3.61/4.40	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.40	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.40	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.40	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.40	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.40	-> Rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	-> Usable rules:
3.61/4.40	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.40	 active(adx(nil)) -> mark(nil)
3.61/4.40	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.40	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.40	 active(incr(nil)) -> mark(nil)
3.61/4.40	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.40	 active(nats) -> mark(adx(zeros))
3.61/4.40	 active(zeros) -> mark(cons(0,zeros))
3.61/4.40	 adx(active(X:S)) -> adx(X:S)
3.61/4.40	 adx(mark(X:S)) -> adx(X:S)
3.61/4.40	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.40	 head(active(X:S)) -> head(X:S)
3.61/4.40	 head(mark(X:S)) -> head(X:S)
3.61/4.40	 incr(active(X:S)) -> incr(X:S)
3.61/4.40	 incr(mark(X:S)) -> incr(X:S)
3.61/4.40	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.40	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.40	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.40	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.40	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.40	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.40	 mark(0) -> active(0)
3.61/4.40	 mark(nats) -> active(nats)
3.61/4.40	 mark(nil) -> active(nil)
3.61/4.40	 mark(zeros) -> active(zeros)
3.61/4.40	 s(active(X:S)) -> s(X:S)
3.61/4.40	 s(mark(X:S)) -> s(X:S)
3.61/4.40	 tail(active(X:S)) -> tail(X:S)
3.61/4.40	 tail(mark(X:S)) -> tail(X:S)
3.61/4.40	->Interpretation type:
3.61/4.40	 Linear
3.61/4.40	->Coefficients:
3.61/4.40	 Natural Numbers
3.61/4.40	->Dimension:
3.61/4.40	 1
3.61/4.40	->Bound:
3.61/4.40	 2
3.61/4.40	->Interpretation:
3.61/4.40	 
3.61/4.40	[active](X) = 0
3.61/4.40	[adx](X) = 1
3.61/4.40	[cons](X1,X2) = 0
3.61/4.40	[head](X) = 0
3.61/4.40	[incr](X) = 1
3.61/4.40	[mark](X) = 0
3.61/4.40	[s](X) = 1
3.61/4.40	[tail](X) = 0
3.61/4.40	[0] = 2
3.61/4.40	[fSNonEmpty] = 0
3.61/4.40	[nats] = 0
3.61/4.40	[nil] = 2
3.61/4.40	[zeros] = 1
3.61/4.40	[ACTIVE](X) = X + 1
3.61/4.40	[ADX](X) = 0
3.61/4.40	[CONS](X1,X2) = 0
3.61/4.40	[HEAD](X) = 0
3.61/4.40	[INCR](X) = 0
3.61/4.40	[MARK](X) = 2
3.61/4.40	[S](X) = 0
3.61/4.40	[TAIL](X) = 0
3.61/4.40	
3.61/4.40	Problem 1.7: 
3.61/4.40	
3.61/4.40	SCC Processor:
3.61/4.40	-> Pairs:
3.61/4.40	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.40	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.40	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.40	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.40	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(head(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = X
3.61/4.41	[adx](X) = 2.X + 2
3.61/4.41	[cons](X1,X2) = 2.X1 + X2
3.61/4.41	[head](X) = 2.X + 1
3.61/4.41	[incr](X) = X
3.61/4.41	[mark](X) = X
3.61/4.41	[s](X) = X
3.61/4.41	[tail](X) = 2.X + 2
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 2
3.61/4.41	[zeros] = 0
3.61/4.41	[ACTIVE](X) = 2.X + 2
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2.X + 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = 2
3.61/4.41	[adx](X) = 1
3.61/4.41	[cons](X1,X2) = 0
3.61/4.41	[head](X) = 2
3.61/4.41	[incr](X) = 1
3.61/4.41	[mark](X) = 2
3.61/4.41	[s](X) = 0
3.61/4.41	[tail](X) = 1
3.61/4.41	[0] = 1
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 1
3.61/4.41	[zeros] = 1
3.61/4.41	[ACTIVE](X) = 2.X
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> ACTIVE(tail(mark(X:S)))
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = 2
3.61/4.41	[adx](X) = 1
3.61/4.41	[cons](X1,X2) = 0
3.61/4.41	[head](X) = 1
3.61/4.41	[incr](X) = 1
3.61/4.41	[mark](X) = 2
3.61/4.41	[s](X) = 2
3.61/4.41	[tail](X) = 0
3.61/4.41	[0] = 1
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 0
3.61/4.41	[zeros] = 1
3.61/4.41	[ACTIVE](X) = 2.X
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(tail(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = X
3.61/4.41	[adx](X) = 2.X
3.61/4.41	[cons](X1,X2) = 2.X1 + 2.X2
3.61/4.41	[head](X) = 2.X + 1
3.61/4.41	[incr](X) = X
3.61/4.41	[mark](X) = X
3.61/4.41	[s](X) = X
3.61/4.41	[tail](X) = 2.X + 1
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 2
3.61/4.41	[zeros] = 0
3.61/4.41	[ACTIVE](X) = 2.X + 2
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2.X + 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(adx(cons(X:S,L:S))) -> MARK(incr(cons(X:S,adx(L:S))))
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 All rationals
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = X
3.61/4.41	[adx](X) = 2.X + 2
3.61/4.41	[cons](X1,X2) = 2.X1 + 1/2.X2
3.61/4.41	[head](X) = 2.X + 2
3.61/4.41	[incr](X) = X + 1/2
3.61/4.41	[mark](X) = X
3.61/4.41	[s](X) = X
3.61/4.41	[tail](X) = 2.X
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 1/2
3.61/4.41	[zeros] = 0
3.61/4.41	[ACTIVE](X) = 1/2.X + 2
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 1/2.X + 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(adx(X:S)) -> ACTIVE(adx(mark(X:S)))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = 2
3.61/4.41	[adx](X) = 0
3.61/4.41	[cons](X1,X2) = 0
3.61/4.41	[head](X) = 2
3.61/4.41	[incr](X) = 2
3.61/4.41	[mark](X) = 2
3.61/4.41	[s](X) = 2
3.61/4.41	[tail](X) = 2
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 1
3.61/4.41	[nil] = 0
3.61/4.41	[zeros] = 2
3.61/4.41	[ACTIVE](X) = X
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(incr(cons(X:S,L:S))) -> MARK(cons(s(X:S),incr(L:S)))
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 All rationals
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = X
3.61/4.41	[adx](X) = 2.X
3.61/4.41	[cons](X1,X2) = 2.X1 + 1/2.X2 + 1/2
3.61/4.41	[head](X) = 2.X + 1/2
3.61/4.41	[incr](X) = X + 1/2
3.61/4.41	[mark](X) = X
3.61/4.41	[s](X) = X
3.61/4.41	[tail](X) = 2.X + 2
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 2
3.61/4.41	[zeros] = 1
3.61/4.41	[ACTIVE](X) = 2.X
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2.X
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> ACTIVE(incr(mark(X:S)))
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = X
3.61/4.41	[adx](X) = X
3.61/4.41	[cons](X1,X2) = 2.X1 + X2
3.61/4.41	[head](X) = X
3.61/4.41	[incr](X) = 0
3.61/4.41	[mark](X) = X
3.61/4.41	[s](X) = 0
3.61/4.41	[tail](X) = 2.X + 2
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 2
3.61/4.41	[nil] = 0
3.61/4.41	[zeros] = 2
3.61/4.41	[ACTIVE](X) = X
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Reduction Pairs Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 ACTIVE(zeros) -> MARK(cons(0,zeros))
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	-> Usable rules:
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	->Interpretation type:
3.61/4.41	 Linear
3.61/4.41	->Coefficients:
3.61/4.41	 Natural Numbers
3.61/4.41	->Dimension:
3.61/4.41	 1
3.61/4.41	->Bound:
3.61/4.41	 2
3.61/4.41	->Interpretation:
3.61/4.41	 
3.61/4.41	[active](X) = 2.X
3.61/4.41	[adx](X) = 0
3.61/4.41	[cons](X1,X2) = 2.X1 + 1
3.61/4.41	[head](X) = 0
3.61/4.41	[incr](X) = 2.X
3.61/4.41	[mark](X) = 2.X
3.61/4.41	[s](X) = 2.X
3.61/4.41	[tail](X) = 0
3.61/4.41	[0] = 0
3.61/4.41	[fSNonEmpty] = 0
3.61/4.41	[nats] = 0
3.61/4.41	[nil] = 0
3.61/4.41	[zeros] = 2
3.61/4.41	[ACTIVE](X) = 2.X
3.61/4.41	[ADX](X) = 0
3.61/4.41	[CONS](X1,X2) = 0
3.61/4.41	[HEAD](X) = 0
3.61/4.41	[INCR](X) = 0
3.61/4.41	[MARK](X) = 2.X + 1
3.61/4.41	[S](X) = 0
3.61/4.41	[TAIL](X) = 0
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(zeros) -> ACTIVE(zeros)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	->->Cycle:
3.61/4.41	->->-> Pairs:
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	->->-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	Subterm Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.61/4.41	 MARK(incr(X:S)) -> MARK(X:S)
3.61/4.41	 MARK(s(X:S)) -> MARK(X:S)
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Projection:
3.61/4.41	 pi(MARK) = 1
3.61/4.41	
3.61/4.41	Problem 1.7: 
3.61/4.41	
3.61/4.41	SCC Processor:
3.61/4.41	-> Pairs:
3.61/4.41	 Empty
3.61/4.41	-> Rules:
3.61/4.41	 active(adx(cons(X:S,L:S))) -> mark(incr(cons(X:S,adx(L:S))))
3.61/4.41	 active(adx(nil)) -> mark(nil)
3.61/4.41	 active(head(cons(X:S,L:S))) -> mark(X:S)
3.61/4.41	 active(incr(cons(X:S,L:S))) -> mark(cons(s(X:S),incr(L:S)))
3.61/4.41	 active(incr(nil)) -> mark(nil)
3.61/4.41	 active(tail(cons(X:S,L:S))) -> mark(L:S)
3.61/4.41	 active(nats) -> mark(adx(zeros))
3.61/4.41	 active(zeros) -> mark(cons(0,zeros))
3.61/4.41	 adx(active(X:S)) -> adx(X:S)
3.61/4.41	 adx(mark(X:S)) -> adx(X:S)
3.61/4.41	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
3.61/4.41	 head(active(X:S)) -> head(X:S)
3.61/4.41	 head(mark(X:S)) -> head(X:S)
3.61/4.41	 incr(active(X:S)) -> incr(X:S)
3.61/4.41	 incr(mark(X:S)) -> incr(X:S)
3.61/4.41	 mark(adx(X:S)) -> active(adx(mark(X:S)))
3.61/4.41	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
3.61/4.41	 mark(head(X:S)) -> active(head(mark(X:S)))
3.61/4.41	 mark(incr(X:S)) -> active(incr(mark(X:S)))
3.61/4.41	 mark(s(X:S)) -> active(s(mark(X:S)))
3.61/4.41	 mark(tail(X:S)) -> active(tail(mark(X:S)))
3.61/4.41	 mark(0) -> active(0)
3.61/4.41	 mark(nats) -> active(nats)
3.61/4.41	 mark(nil) -> active(nil)
3.61/4.41	 mark(zeros) -> active(zeros)
3.61/4.41	 s(active(X:S)) -> s(X:S)
3.61/4.41	 s(mark(X:S)) -> s(X:S)
3.61/4.41	 tail(active(X:S)) -> tail(X:S)
3.61/4.41	 tail(mark(X:S)) -> tail(X:S)
3.61/4.41	->Strongly Connected Components:
3.61/4.41	 There is no strongly connected component
3.61/4.41	
3.61/4.41	The problem is finite.
3.61/4.41	EOF