0.65/0.68	YES
0.65/0.68	
0.65/0.68	Problem 1: 
0.65/0.68	
0.65/0.68	(VAR v_NonEmpty:S X:S X1:S X2:S X3:S Y:S Z:S)
0.65/0.68	(RULES
0.65/0.68	active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.68	active(add(0,X:S)) -> mark(X:S)
0.65/0.68	active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.68	active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.68	active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.68	active(first(0,X:S)) -> mark(nil)
0.65/0.68	active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.68	active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.68	active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.68	add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.68	add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.68	add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.68	add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.68	and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.68	and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.68	and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.68	and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.68	cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.68	cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.68	cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.68	cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.68	first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.68	first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.68	first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.68	first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.68	from(active(X:S)) -> from(X:S)
0.65/0.68	from(mark(X:S)) -> from(X:S)
0.65/0.68	if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.68	if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.68	if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.68	if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.68	if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.68	if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.68	mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.68	mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.68	mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.68	mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.68	mark(from(X:S)) -> active(from(X:S))
0.65/0.68	mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.68	mark(s(X:S)) -> active(s(X:S))
0.65/0.68	mark(0) -> active(0)
0.65/0.68	mark(ffalse) -> active(ffalse)
0.65/0.68	mark(nil) -> active(nil)
0.65/0.68	mark(ttrue) -> active(ttrue)
0.65/0.68	s(active(X:S)) -> s(X:S)
0.65/0.68	s(mark(X:S)) -> s(X:S)
0.65/0.68	) 
0.65/0.68	(STRATEGY INNERMOST)
0.65/0.68	
0.65/0.68	Problem 1: 
0.65/0.68	
0.65/0.68	Dependency Pairs Processor:
0.65/0.68	-> Pairs:
0.65/0.68	 ACTIVE(add(s(X:S),Y:S)) -> ADD(X:S,Y:S)
0.65/0.68	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.65/0.68	 ACTIVE(add(s(X:S),Y:S)) -> S(add(X:S,Y:S))
0.65/0.68	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.68	 ACTIVE(and(ffalse,Y:S)) -> MARK(ffalse)
0.65/0.68	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.68	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> CONS(Y:S,first(X:S,Z:S))
0.65/0.68	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> FIRST(X:S,Z:S)
0.65/0.68	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.68	 ACTIVE(first(0,X:S)) -> MARK(nil)
0.65/0.68	 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S)))
0.65/0.68	 ACTIVE(from(X:S)) -> FROM(s(X:S))
0.65/0.68	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.68	 ACTIVE(from(X:S)) -> S(X:S)
0.65/0.68	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.68	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.68	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.68	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.68	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.68	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.68	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.68	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.68	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.68	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.68	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.68	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.68	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.68	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.68	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.68	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.68	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.68	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.68	 FROM(active(X:S)) -> FROM(X:S)
0.65/0.68	 FROM(mark(X:S)) -> FROM(X:S)
0.65/0.68	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.68	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.68	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.68	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.68	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.68	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.68	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.68	 MARK(add(X1:S,X2:S)) -> ADD(mark(X1:S),X2:S)
0.65/0.68	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.68	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.68	 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S)
0.65/0.68	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.68	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(X1:S,X2:S))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> FIRST(mark(X1:S),mark(X2:S))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.69	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> IF(mark(X1:S),X2:S,X3:S)
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.69	 MARK(s(X:S)) -> ACTIVE(s(X:S))
0.65/0.69	 S(active(X:S)) -> S(X:S)
0.65/0.69	 S(mark(X:S)) -> S(X:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	Problem 1: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 ACTIVE(add(s(X:S),Y:S)) -> ADD(X:S,Y:S)
0.65/0.69	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.65/0.69	 ACTIVE(add(s(X:S),Y:S)) -> S(add(X:S,Y:S))
0.65/0.69	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.69	 ACTIVE(and(ffalse,Y:S)) -> MARK(ffalse)
0.65/0.69	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.69	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> CONS(Y:S,first(X:S,Z:S))
0.65/0.69	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> FIRST(X:S,Z:S)
0.65/0.69	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 ACTIVE(first(0,X:S)) -> MARK(nil)
0.65/0.69	 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S)))
0.65/0.69	 ACTIVE(from(X:S)) -> FROM(s(X:S))
0.65/0.69	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.69	 ACTIVE(from(X:S)) -> S(X:S)
0.65/0.69	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.69	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.69	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.69	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.69	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FROM(active(X:S)) -> FROM(X:S)
0.65/0.69	 FROM(mark(X:S)) -> FROM(X:S)
0.65/0.69	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.69	 MARK(add(X1:S,X2:S)) -> ADD(mark(X1:S),X2:S)
0.65/0.69	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.69	 MARK(and(X1:S,X2:S)) -> AND(mark(X1:S),X2:S)
0.65/0.69	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(X1:S,X2:S))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> FIRST(mark(X1:S),mark(X2:S))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.69	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> IF(mark(X1:S),X2:S,X3:S)
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.69	 MARK(s(X:S)) -> ACTIVE(s(X:S))
0.65/0.69	 S(active(X:S)) -> S(X:S)
0.65/0.69	 S(mark(X:S)) -> S(X:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 S(active(X:S)) -> S(X:S)
0.65/0.69	 S(mark(X:S)) -> S(X:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 FROM(active(X:S)) -> FROM(X:S)
0.65/0.69	 FROM(mark(X:S)) -> FROM(X:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.69	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.65/0.69	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.69	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.69	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.69	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.69	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.69	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.69	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.69	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.69	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.69	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	
0.65/0.69	The problem is decomposed in 8 subproblems.
0.65/0.69	
0.65/0.69	Problem 1.1: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 S(active(X:S)) -> S(X:S)
0.65/0.69	 S(mark(X:S)) -> S(X:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(S) = 1
0.65/0.69	
0.65/0.69	Problem 1.1: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 Empty
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	 There is no strongly connected component
0.65/0.69	
0.65/0.69	The problem is finite.
0.65/0.69	
0.65/0.69	Problem 1.2: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 IF(active(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(mark(X1:S),X2:S,X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(IF) = 1
0.65/0.69	
0.65/0.69	Problem 1.2: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	Problem 1.2: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 IF(X1:S,active(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,mark(X2:S),X3:S) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(IF) = 2
0.65/0.69	
0.65/0.69	Problem 1.2: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	Problem 1.2: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 IF(X1:S,X2:S,active(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	 IF(X1:S,X2:S,mark(X3:S)) -> IF(X1:S,X2:S,X3:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(IF) = 3
0.65/0.69	
0.65/0.69	Problem 1.2: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 Empty
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	 There is no strongly connected component
0.65/0.69	
0.65/0.69	The problem is finite.
0.65/0.69	
0.65/0.69	Problem 1.3: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 FROM(active(X:S)) -> FROM(X:S)
0.65/0.69	 FROM(mark(X:S)) -> FROM(X:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(FROM) = 1
0.65/0.69	
0.65/0.69	Problem 1.3: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 Empty
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	 There is no strongly connected component
0.65/0.69	
0.65/0.69	The problem is finite.
0.65/0.69	
0.65/0.69	Problem 1.4: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(FIRST) = 1
0.65/0.69	
0.65/0.69	Problem 1.4: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	Problem 1.4: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(FIRST) = 2
0.65/0.69	
0.65/0.69	Problem 1.4: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 Empty
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	 There is no strongly connected component
0.65/0.69	
0.65/0.69	The problem is finite.
0.65/0.69	
0.65/0.69	Problem 1.5: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(CONS) = 1
0.65/0.69	
0.65/0.69	Problem 1.5: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	Problem 1.5: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(CONS) = 2
0.65/0.69	
0.65/0.69	Problem 1.5: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 Empty
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	 There is no strongly connected component
0.65/0.69	
0.65/0.69	The problem is finite.
0.65/0.69	
0.65/0.69	Problem 1.6: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 AND(active(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.69	 AND(mark(X1:S),X2:S) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(AND) = 1
0.65/0.69	
0.65/0.69	Problem 1.6: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	->->Cycle:
0.65/0.69	->->-> Pairs:
0.65/0.69	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	->->-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	
0.65/0.69	Problem 1.6: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 AND(X1:S,active(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	 AND(X1:S,mark(X2:S)) -> AND(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Projection:
0.65/0.69	 pi(AND) = 2
0.65/0.69	
0.65/0.69	Problem 1.6: 
0.65/0.69	
0.65/0.69	SCC Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 Empty
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.69	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.69	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.69	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.69	 mark(from(X:S)) -> active(from(X:S))
0.65/0.69	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.69	 mark(s(X:S)) -> active(s(X:S))
0.65/0.69	 mark(0) -> active(0)
0.65/0.69	 mark(ffalse) -> active(ffalse)
0.65/0.69	 mark(nil) -> active(nil)
0.65/0.69	 mark(ttrue) -> active(ttrue)
0.65/0.69	 s(active(X:S)) -> s(X:S)
0.65/0.69	 s(mark(X:S)) -> s(X:S)
0.65/0.69	->Strongly Connected Components:
0.65/0.69	 There is no strongly connected component
0.65/0.69	
0.65/0.69	The problem is finite.
0.65/0.69	
0.65/0.69	Problem 1.7: 
0.65/0.69	
0.65/0.69	Subterm Processor:
0.65/0.69	-> Pairs:
0.65/0.69	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.69	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.69	-> Rules:
0.65/0.69	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.69	 active(add(0,X:S)) -> mark(X:S)
0.65/0.69	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.69	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.69	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.69	 active(first(0,X:S)) -> mark(nil)
0.65/0.69	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.69	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.69	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.69	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.69	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.69	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.69	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.69	 from(active(X:S)) -> from(X:S)
0.65/0.69	 from(mark(X:S)) -> from(X:S)
0.65/0.69	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.69	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Projection:
0.65/0.70	 pi(ADD) = 1
0.65/0.70	
0.65/0.70	Problem 1.7: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.70	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.70	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.7: 
0.65/0.70	
0.65/0.70	Subterm Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.70	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Projection:
0.65/0.70	 pi(ADD) = 2
0.65/0.70	
0.65/0.70	Problem 1.7: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 Empty
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	 There is no strongly connected component
0.65/0.70	
0.65/0.70	The problem is finite.
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.65/0.70	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X
0.65/0.70	[add](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = 0
0.65/0.70	[first](X1,X2) = X1 + 2.X2 + 2
0.65/0.70	[from](X) = X + 2
0.65/0.70	[if](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
0.65/0.70	[mark](X) = 2.X + 1
0.65/0.70	[s](X) = 2
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 2
0.65/0.70	[nil] = 1
0.65/0.70	[true] = 0
0.65/0.70	[ACTIVE](X) = X + 1
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X + 2
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X
0.65/0.70	[add](X1,X2) = 2.X1 + 2.X2 + 1
0.65/0.70	[and](X1,X2) = X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = 0
0.65/0.70	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[from](X) = 2.X + 2
0.65/0.70	[if](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
0.65/0.70	[mark](X) = 2.X
0.65/0.70	[s](X) = 2
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 2
0.65/0.70	[nil] = 0
0.65/0.70	[true] = 2
0.65/0.70	[ACTIVE](X) = X + 2
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X + 2
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(and(ttrue,X:S)) -> MARK(X:S)
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X + 2
0.65/0.70	[add](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = X1 + 2
0.65/0.70	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[from](X) = 2.X + 2
0.65/0.70	[if](X1,X2,X3) = X1 + 2.X2 + 2.X3 + 2
0.65/0.70	[mark](X) = 2.X
0.65/0.70	[s](X) = 2
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 2
0.65/0.70	[nil] = 2
0.65/0.70	[true] = 2
0.65/0.70	[ACTIVE](X) = X + 2
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X + 2
0.65/0.70	[add](X1,X2) = X1 + 2.X2 + 2
0.65/0.70	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = X1 + 2
0.65/0.70	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[from](X) = 2.X + 2
0.65/0.70	[if](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.65/0.70	[mark](X) = 2.X
0.65/0.70	[s](X) = 2
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 2
0.65/0.70	[nil] = 2
0.65/0.70	[true] = 2
0.65/0.70	[ACTIVE](X) = X + 2
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X
0.65/0.70	[add](X1,X2) = 2.X1 + 2.X2 + 1
0.65/0.70	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = 0
0.65/0.70	[first](X1,X2) = 2.X1 + X2 + 2
0.65/0.70	[from](X) = 2
0.65/0.70	[if](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.65/0.70	[mark](X) = 2.X + 1
0.65/0.70	[s](X) = 1
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 2
0.65/0.70	[nil] = 2
0.65/0.70	[true] = 1
0.65/0.70	[ACTIVE](X) = X + 1
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X + 2
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(from(X:S)) -> ACTIVE(from(X:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(if(ffalse,X:S,Y:S)) -> MARK(Y:S)
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X
0.65/0.70	[add](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = 0
0.65/0.70	[first](X1,X2) = X1 + X2 + 2
0.65/0.70	[from](X) = 2
0.65/0.70	[if](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.65/0.70	[mark](X) = 2.X + 2
0.65/0.70	[s](X) = 2
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 2
0.65/0.70	[nil] = 1
0.65/0.70	[true] = 2
0.65/0.70	[ACTIVE](X) = X
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X + 2
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	Reduction Pairs Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 ACTIVE(if(ttrue,X:S,Y:S)) -> MARK(X:S)
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	-> Usable rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Interpretation type:
0.65/0.70	 Linear
0.65/0.70	->Coefficients:
0.65/0.70	 Natural Numbers
0.65/0.70	->Dimension:
0.65/0.70	 1
0.65/0.70	->Bound:
0.65/0.70	 2
0.65/0.70	->Interpretation:
0.65/0.70	 
0.65/0.70	[active](X) = X
0.65/0.70	[add](X1,X2) = X1 + 2.X2 + 2
0.65/0.70	[and](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[cons](X1,X2) = X1 + 1
0.65/0.70	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.65/0.70	[from](X) = 2.X + 2
0.65/0.70	[if](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.65/0.70	[mark](X) = 2.X
0.65/0.70	[s](X) = 2
0.65/0.70	[0] = 2
0.65/0.70	[fSNonEmpty] = 0
0.65/0.70	[false] = 0
0.65/0.70	[nil] = 2
0.65/0.70	[true] = 2
0.65/0.70	[ACTIVE](X) = X + 2
0.65/0.70	[ADD](X1,X2) = 0
0.65/0.70	[AND](X1,X2) = 0
0.65/0.70	[CONS](X1,X2) = 0
0.65/0.70	[FIRST](X1,X2) = 0
0.65/0.70	[FROM](X) = 0
0.65/0.70	[IF](X1,X2,X3) = 0
0.65/0.70	[MARK](X) = 2.X + 1
0.65/0.70	[S](X) = 0
0.65/0.70	
0.65/0.70	Problem 1.8: 
0.65/0.70	
0.65/0.70	SCC Processor:
0.65/0.70	-> Pairs:
0.65/0.70	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),X2:S))
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> ACTIVE(and(mark(X1:S),X2:S))
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> ACTIVE(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.70	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.70	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.70	 mark(from(X:S)) -> active(from(X:S))
0.65/0.70	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.70	 mark(s(X:S)) -> active(s(X:S))
0.65/0.70	 mark(0) -> active(0)
0.65/0.70	 mark(ffalse) -> active(ffalse)
0.65/0.70	 mark(nil) -> active(nil)
0.65/0.70	 mark(ttrue) -> active(ttrue)
0.65/0.70	 s(active(X:S)) -> s(X:S)
0.65/0.70	 s(mark(X:S)) -> s(X:S)
0.65/0.70	->Strongly Connected Components:
0.65/0.70	->->Cycle:
0.65/0.70	->->-> Pairs:
0.65/0.70	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.70	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.70	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.70	->->-> Rules:
0.65/0.70	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.70	 active(add(0,X:S)) -> mark(X:S)
0.65/0.70	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.70	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.70	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.70	 active(first(0,X:S)) -> mark(nil)
0.65/0.70	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.70	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.70	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.70	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.70	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.70	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.70	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.70	 from(active(X:S)) -> from(X:S)
0.65/0.70	 from(mark(X:S)) -> from(X:S)
0.65/0.70	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.70	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.70	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.71	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.71	 mark(from(X:S)) -> active(from(X:S))
0.65/0.71	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.71	 mark(s(X:S)) -> active(s(X:S))
0.65/0.71	 mark(0) -> active(0)
0.65/0.71	 mark(ffalse) -> active(ffalse)
0.65/0.71	 mark(nil) -> active(nil)
0.65/0.71	 mark(ttrue) -> active(ttrue)
0.65/0.71	 s(active(X:S)) -> s(X:S)
0.65/0.71	 s(mark(X:S)) -> s(X:S)
0.65/0.71	
0.65/0.71	Problem 1.8: 
0.65/0.71	
0.65/0.71	Subterm Processor:
0.65/0.71	-> Pairs:
0.65/0.71	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.71	 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.71	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.65/0.71	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.65/0.71	 MARK(if(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.65/0.71	-> Rules:
0.65/0.71	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.71	 active(add(0,X:S)) -> mark(X:S)
0.65/0.71	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.71	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.71	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.71	 active(first(0,X:S)) -> mark(nil)
0.65/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.71	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.71	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.71	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.71	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.71	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.71	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.71	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.71	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.71	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.71	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.71	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.71	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.71	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.71	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.71	 from(active(X:S)) -> from(X:S)
0.65/0.71	 from(mark(X:S)) -> from(X:S)
0.65/0.71	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.71	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.71	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.71	 mark(from(X:S)) -> active(from(X:S))
0.65/0.71	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.71	 mark(s(X:S)) -> active(s(X:S))
0.65/0.71	 mark(0) -> active(0)
0.65/0.71	 mark(ffalse) -> active(ffalse)
0.65/0.71	 mark(nil) -> active(nil)
0.65/0.71	 mark(ttrue) -> active(ttrue)
0.65/0.71	 s(active(X:S)) -> s(X:S)
0.65/0.71	 s(mark(X:S)) -> s(X:S)
0.65/0.71	->Projection:
0.65/0.71	 pi(MARK) = 1
0.65/0.71	
0.65/0.71	Problem 1.8: 
0.65/0.71	
0.65/0.71	SCC Processor:
0.65/0.71	-> Pairs:
0.65/0.71	 Empty
0.65/0.71	-> Rules:
0.65/0.71	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.65/0.71	 active(add(0,X:S)) -> mark(X:S)
0.65/0.71	 active(and(ffalse,Y:S)) -> mark(ffalse)
0.65/0.71	 active(and(ttrue,X:S)) -> mark(X:S)
0.65/0.71	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.65/0.71	 active(first(0,X:S)) -> mark(nil)
0.65/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.65/0.71	 active(if(ffalse,X:S,Y:S)) -> mark(Y:S)
0.65/0.71	 active(if(ttrue,X:S,Y:S)) -> mark(X:S)
0.65/0.71	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.71	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.65/0.71	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.65/0.71	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.65/0.71	 and(active(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.71	 and(mark(X1:S),X2:S) -> and(X1:S,X2:S)
0.65/0.71	 and(X1:S,active(X2:S)) -> and(X1:S,X2:S)
0.65/0.71	 and(X1:S,mark(X2:S)) -> and(X1:S,X2:S)
0.65/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.65/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.65/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.65/0.71	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.71	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.65/0.71	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.65/0.71	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.65/0.71	 from(active(X:S)) -> from(X:S)
0.65/0.71	 from(mark(X:S)) -> from(X:S)
0.65/0.71	 if(active(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(mark(X1:S),X2:S,X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,active(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,mark(X2:S),X3:S) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,X2:S,active(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 if(X1:S,X2:S,mark(X3:S)) -> if(X1:S,X2:S,X3:S)
0.65/0.71	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),X2:S))
0.65/0.71	 mark(and(X1:S,X2:S)) -> active(and(mark(X1:S),X2:S))
0.65/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(X1:S,X2:S))
0.65/0.71	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.65/0.71	 mark(from(X:S)) -> active(from(X:S))
0.65/0.71	 mark(if(X1:S,X2:S,X3:S)) -> active(if(mark(X1:S),X2:S,X3:S))
0.65/0.71	 mark(s(X:S)) -> active(s(X:S))
0.65/0.71	 mark(0) -> active(0)
0.65/0.71	 mark(ffalse) -> active(ffalse)
0.65/0.71	 mark(nil) -> active(nil)
0.65/0.71	 mark(ttrue) -> active(ttrue)
0.65/0.71	 s(active(X:S)) -> s(X:S)
0.65/0.71	 s(mark(X:S)) -> s(X:S)
0.65/0.71	->Strongly Connected Components:
0.65/0.71	 There is no strongly connected component
0.65/0.71	
0.65/0.71	The problem is finite.
0.65/0.71	EOF