0.64/0.71	YES
0.64/0.71	
0.64/0.71	Problem 1: 
0.64/0.71	
0.64/0.71	(VAR v_NonEmpty:S X:S X1:S X2:S Y:S)
0.64/0.71	(RULES
0.64/0.71	active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	active(length(nil)) -> mark(0)
0.64/0.71	active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	from(active(X:S)) -> from(X:S)
0.64/0.71	from(mark(X:S)) -> from(X:S)
0.64/0.71	length(active(X:S)) -> length(X:S)
0.64/0.71	length(mark(X:S)) -> length(X:S)
0.64/0.71	length1(active(X:S)) -> length1(X:S)
0.64/0.71	length1(mark(X:S)) -> length1(X:S)
0.64/0.71	mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	mark(length(X:S)) -> active(length(X:S))
0.64/0.71	mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	mark(0) -> active(0)
0.64/0.71	mark(nil) -> active(nil)
0.64/0.71	s(active(X:S)) -> s(X:S)
0.64/0.71	s(mark(X:S)) -> s(X:S)
0.64/0.71	) 
0.64/0.71	(STRATEGY INNERMOST)
0.64/0.71	
0.64/0.71	Problem 1: 
0.64/0.71	
0.64/0.71	Dependency Pairs Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S)))
0.64/0.71	 ACTIVE(from(X:S)) -> FROM(s(X:S))
0.64/0.71	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.64/0.71	 ACTIVE(from(X:S)) -> S(X:S)
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> LENGTH1(Y:S)
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> S(length1(Y:S))
0.64/0.71	 ACTIVE(length(nil)) -> MARK(0)
0.64/0.71	 ACTIVE(length1(X:S)) -> LENGTH(X:S)
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 FROM(active(X:S)) -> FROM(X:S)
0.64/0.71	 FROM(mark(X:S)) -> FROM(X:S)
0.64/0.71	 LENGTH(active(X:S)) -> LENGTH(X:S)
0.64/0.71	 LENGTH(mark(X:S)) -> LENGTH(X:S)
0.64/0.71	 LENGTH1(active(X:S)) -> LENGTH1(X:S)
0.64/0.71	 LENGTH1(mark(X:S)) -> LENGTH1(X:S)
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> FROM(mark(X:S))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(s(X:S)) -> S(mark(X:S))
0.64/0.71	 S(active(X:S)) -> S(X:S)
0.64/0.71	 S(mark(X:S)) -> S(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	Problem 1: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(from(X:S)) -> CONS(X:S,from(s(X:S)))
0.64/0.71	 ACTIVE(from(X:S)) -> FROM(s(X:S))
0.64/0.71	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.64/0.71	 ACTIVE(from(X:S)) -> S(X:S)
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> LENGTH1(Y:S)
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> S(length1(Y:S))
0.64/0.71	 ACTIVE(length(nil)) -> MARK(0)
0.64/0.71	 ACTIVE(length1(X:S)) -> LENGTH(X:S)
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 FROM(active(X:S)) -> FROM(X:S)
0.64/0.71	 FROM(mark(X:S)) -> FROM(X:S)
0.64/0.71	 LENGTH(active(X:S)) -> LENGTH(X:S)
0.64/0.71	 LENGTH(mark(X:S)) -> LENGTH(X:S)
0.64/0.71	 LENGTH1(active(X:S)) -> LENGTH1(X:S)
0.64/0.71	 LENGTH1(mark(X:S)) -> LENGTH1(X:S)
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> FROM(mark(X:S))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(s(X:S)) -> S(mark(X:S))
0.64/0.71	 S(active(X:S)) -> S(X:S)
0.64/0.71	 S(mark(X:S)) -> S(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 S(active(X:S)) -> S(X:S)
0.64/0.71	 S(mark(X:S)) -> S(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 LENGTH1(active(X:S)) -> LENGTH1(X:S)
0.64/0.71	 LENGTH1(mark(X:S)) -> LENGTH1(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 LENGTH(active(X:S)) -> LENGTH(X:S)
0.64/0.71	 LENGTH(mark(X:S)) -> LENGTH(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 FROM(active(X:S)) -> FROM(X:S)
0.64/0.71	 FROM(mark(X:S)) -> FROM(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	
0.64/0.71	The problem is decomposed in 6 subproblems.
0.64/0.71	
0.64/0.71	Problem 1.1: 
0.64/0.71	
0.64/0.71	Subterm Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 S(active(X:S)) -> S(X:S)
0.64/0.71	 S(mark(X:S)) -> S(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Projection:
0.64/0.71	 pi(S) = 1
0.64/0.71	
0.64/0.71	Problem 1.1: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 Empty
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	 There is no strongly connected component
0.64/0.71	
0.64/0.71	The problem is finite.
0.64/0.71	
0.64/0.71	Problem 1.2: 
0.64/0.71	
0.64/0.71	Subterm Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 LENGTH1(active(X:S)) -> LENGTH1(X:S)
0.64/0.71	 LENGTH1(mark(X:S)) -> LENGTH1(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Projection:
0.64/0.71	 pi(LENGTH1) = 1
0.64/0.71	
0.64/0.71	Problem 1.2: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 Empty
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	 There is no strongly connected component
0.64/0.71	
0.64/0.71	The problem is finite.
0.64/0.71	
0.64/0.71	Problem 1.3: 
0.64/0.71	
0.64/0.71	Subterm Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 LENGTH(active(X:S)) -> LENGTH(X:S)
0.64/0.71	 LENGTH(mark(X:S)) -> LENGTH(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Projection:
0.64/0.71	 pi(LENGTH) = 1
0.64/0.71	
0.64/0.71	Problem 1.3: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 Empty
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	 There is no strongly connected component
0.64/0.71	
0.64/0.71	The problem is finite.
0.64/0.71	
0.64/0.71	Problem 1.4: 
0.64/0.71	
0.64/0.71	Subterm Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 FROM(active(X:S)) -> FROM(X:S)
0.64/0.71	 FROM(mark(X:S)) -> FROM(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Projection:
0.64/0.71	 pi(FROM) = 1
0.64/0.71	
0.64/0.71	Problem 1.4: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 Empty
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	 There is no strongly connected component
0.64/0.71	
0.64/0.71	The problem is finite.
0.64/0.71	
0.64/0.71	Problem 1.5: 
0.64/0.71	
0.64/0.71	Subterm Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Projection:
0.64/0.71	 pi(CONS) = 1
0.64/0.71	
0.64/0.71	Problem 1.5: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	Problem 1.5: 
0.64/0.71	
0.64/0.71	Subterm Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Projection:
0.64/0.71	 pi(CONS) = 2
0.64/0.71	
0.64/0.71	Problem 1.5: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 Empty
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	 There is no strongly connected component
0.64/0.71	
0.64/0.71	The problem is finite.
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	Reduction Pairs Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(from(X:S)) -> MARK(cons(X:S,from(s(X:S))))
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	-> Usable rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Interpretation type:
0.64/0.71	 Linear
0.64/0.71	->Coefficients:
0.64/0.71	 Natural Numbers
0.64/0.71	->Dimension:
0.64/0.71	 1
0.64/0.71	->Bound:
0.64/0.71	 2
0.64/0.71	->Interpretation:
0.64/0.71	 
0.64/0.71	[active](X) = X
0.64/0.71	[cons](X1,X2) = 2.X1 + 1
0.64/0.71	[from](X) = 2.X + 2
0.64/0.71	[length](X) = 0
0.64/0.71	[length1](X) = 0
0.64/0.71	[mark](X) = X
0.64/0.71	[s](X) = 2.X
0.64/0.71	[0] = 0
0.64/0.71	[fSNonEmpty] = 0
0.64/0.71	[nil] = 2
0.64/0.71	[ACTIVE](X) = 2.X
0.64/0.71	[CONS](X1,X2) = 0
0.64/0.71	[FROM](X) = 0
0.64/0.71	[LENGTH](X) = 0
0.64/0.71	[LENGTH1](X) = 0
0.64/0.71	[MARK](X) = 2.X
0.64/0.71	[S](X) = 0
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	Reduction Pairs Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	-> Usable rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Interpretation type:
0.64/0.71	 Linear
0.64/0.71	->Coefficients:
0.64/0.71	 Natural Numbers
0.64/0.71	->Dimension:
0.64/0.71	 1
0.64/0.71	->Bound:
0.64/0.71	 2
0.64/0.71	->Interpretation:
0.64/0.71	 
0.64/0.71	[active](X) = 0
0.64/0.71	[cons](X1,X2) = 0
0.64/0.71	[from](X) = 0
0.64/0.71	[length](X) = 2
0.64/0.71	[length1](X) = 2
0.64/0.71	[mark](X) = 0
0.64/0.71	[s](X) = 2
0.64/0.71	[0] = 2
0.64/0.71	[fSNonEmpty] = 0
0.64/0.71	[nil] = 2
0.64/0.71	[ACTIVE](X) = X
0.64/0.71	[CONS](X1,X2) = 0
0.64/0.71	[FROM](X) = 0
0.64/0.71	[LENGTH](X) = 0
0.64/0.71	[LENGTH1](X) = 0
0.64/0.71	[MARK](X) = 2
0.64/0.71	[S](X) = 0
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	Reduction Pairs Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	-> Usable rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Interpretation type:
0.64/0.71	 Linear
0.64/0.71	->Coefficients:
0.64/0.71	 Natural Numbers
0.64/0.71	->Dimension:
0.64/0.71	 1
0.64/0.71	->Bound:
0.64/0.71	 2
0.64/0.71	->Interpretation:
0.64/0.71	 
0.64/0.71	[active](X) = X
0.64/0.71	[cons](X1,X2) = X1 + 1
0.64/0.71	[from](X) = 2.X + 2
0.64/0.71	[length](X) = 0
0.64/0.71	[length1](X) = 0
0.64/0.71	[mark](X) = 2.X
0.64/0.71	[s](X) = 2.X
0.64/0.71	[0] = 0
0.64/0.71	[fSNonEmpty] = 0
0.64/0.71	[nil] = 1
0.64/0.71	[ACTIVE](X) = 2
0.64/0.71	[CONS](X1,X2) = 0
0.64/0.71	[FROM](X) = 0
0.64/0.71	[LENGTH](X) = 0
0.64/0.71	[LENGTH1](X) = 0
0.64/0.71	[MARK](X) = X + 2
0.64/0.71	[S](X) = 0
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	Reduction Pairs Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(from(X:S)) -> ACTIVE(from(mark(X:S)))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	-> Usable rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Interpretation type:
0.64/0.71	 Linear
0.64/0.71	->Coefficients:
0.64/0.71	 Natural Numbers
0.64/0.71	->Dimension:
0.64/0.71	 1
0.64/0.71	->Bound:
0.64/0.71	 2
0.64/0.71	->Interpretation:
0.64/0.71	 
0.64/0.71	[active](X) = 2.X + 2
0.64/0.71	[cons](X1,X2) = 0
0.64/0.71	[from](X) = 0
0.64/0.71	[length](X) = 1
0.64/0.71	[length1](X) = 1
0.64/0.71	[mark](X) = 2.X + 2
0.64/0.71	[s](X) = 0
0.64/0.71	[0] = 1
0.64/0.71	[fSNonEmpty] = 0
0.64/0.71	[nil] = 2
0.64/0.71	[ACTIVE](X) = X + 1
0.64/0.71	[CONS](X1,X2) = 0
0.64/0.71	[FROM](X) = 0
0.64/0.71	[LENGTH](X) = 0
0.64/0.71	[LENGTH1](X) = 0
0.64/0.71	[MARK](X) = 2
0.64/0.71	[S](X) = 0
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Strongly Connected Components:
0.64/0.71	->->Cycle:
0.64/0.71	->->-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	->->-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	Reduction Pairs Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(from(X:S)) -> MARK(X:S)
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	-> Usable rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.71	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.71	 from(active(X:S)) -> from(X:S)
0.64/0.71	 from(mark(X:S)) -> from(X:S)
0.64/0.71	 length(active(X:S)) -> length(X:S)
0.64/0.71	 length(mark(X:S)) -> length(X:S)
0.64/0.71	 length1(active(X:S)) -> length1(X:S)
0.64/0.71	 length1(mark(X:S)) -> length1(X:S)
0.64/0.71	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.71	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.71	 mark(length(X:S)) -> active(length(X:S))
0.64/0.71	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.71	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.71	 mark(0) -> active(0)
0.64/0.71	 mark(nil) -> active(nil)
0.64/0.71	 s(active(X:S)) -> s(X:S)
0.64/0.71	 s(mark(X:S)) -> s(X:S)
0.64/0.71	->Interpretation type:
0.64/0.71	 Linear
0.64/0.71	->Coefficients:
0.64/0.71	 Natural Numbers
0.64/0.71	->Dimension:
0.64/0.71	 1
0.64/0.71	->Bound:
0.64/0.71	 2
0.64/0.71	->Interpretation:
0.64/0.71	 
0.64/0.71	[active](X) = X
0.64/0.71	[cons](X1,X2) = X2
0.64/0.71	[from](X) = X + 2
0.64/0.71	[length](X) = 1
0.64/0.71	[length1](X) = 1
0.64/0.71	[mark](X) = X
0.64/0.71	[s](X) = X
0.64/0.71	[0] = 1
0.64/0.71	[fSNonEmpty] = 0
0.64/0.71	[nil] = 2
0.64/0.71	[ACTIVE](X) = 2.X + 2
0.64/0.71	[CONS](X1,X2) = 0
0.64/0.71	[FROM](X) = 0
0.64/0.71	[LENGTH](X) = 0
0.64/0.71	[LENGTH1](X) = 0
0.64/0.71	[MARK](X) = 2.X + 2
0.64/0.71	[S](X) = 0
0.64/0.71	
0.64/0.71	Problem 1.6: 
0.64/0.71	
0.64/0.71	SCC Processor:
0.64/0.71	-> Pairs:
0.64/0.71	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.71	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.71	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.71	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.71	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.71	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.71	-> Rules:
0.64/0.71	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.71	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.71	 active(length(nil)) -> mark(0)
0.64/0.71	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Strongly Connected Components:
0.64/0.72	->->Cycle:
0.64/0.72	->->-> Pairs:
0.64/0.72	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	->->-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	Reduction Pairs Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> ACTIVE(s(mark(X:S)))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	-> Usable rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Interpretation type:
0.64/0.72	 Linear
0.64/0.72	->Coefficients:
0.64/0.72	 Natural Numbers
0.64/0.72	->Dimension:
0.64/0.72	 1
0.64/0.72	->Bound:
0.64/0.72	 2
0.64/0.72	->Interpretation:
0.64/0.72	 
0.64/0.72	[active](X) = 2
0.64/0.72	[cons](X1,X2) = 2
0.64/0.72	[from](X) = 2
0.64/0.72	[length](X) = 2
0.64/0.72	[length1](X) = 2
0.64/0.72	[mark](X) = 2
0.64/0.72	[s](X) = 0
0.64/0.72	[0] = 0
0.64/0.72	[fSNonEmpty] = 0
0.64/0.72	[nil] = 2
0.64/0.72	[ACTIVE](X) = X
0.64/0.72	[CONS](X1,X2) = 0
0.64/0.72	[FROM](X) = 0
0.64/0.72	[LENGTH](X) = 0
0.64/0.72	[LENGTH1](X) = 0
0.64/0.72	[MARK](X) = 2
0.64/0.72	[S](X) = 0
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	SCC Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Strongly Connected Components:
0.64/0.72	->->Cycle:
0.64/0.72	->->-> Pairs:
0.64/0.72	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	->->-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	Reduction Pairs Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 ACTIVE(length(cons(X:S,Y:S))) -> MARK(s(length1(Y:S)))
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	-> Usable rules:
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Interpretation type:
0.64/0.72	 Linear
0.64/0.72	->Coefficients:
0.64/0.72	 Natural Numbers
0.64/0.72	->Dimension:
0.64/0.72	 1
0.64/0.72	->Bound:
0.64/0.72	 2
0.64/0.72	->Interpretation:
0.64/0.72	 
0.64/0.72	[active](X) = 2.X
0.64/0.72	[cons](X1,X2) = 2.X2 + 2
0.64/0.72	[from](X) = 0
0.64/0.72	[length](X) = 2.X + 2
0.64/0.72	[length1](X) = 2.X + 2
0.64/0.72	[mark](X) = 2.X
0.64/0.72	[s](X) = 2.X + 1
0.64/0.72	[0] = 0
0.64/0.72	[fSNonEmpty] = 0
0.64/0.72	[nil] = 0
0.64/0.72	[ACTIVE](X) = 2.X + 2
0.64/0.72	[CONS](X1,X2) = 0
0.64/0.72	[FROM](X) = 0
0.64/0.72	[LENGTH](X) = 0
0.64/0.72	[LENGTH1](X) = 0
0.64/0.72	[MARK](X) = 2.X + 2
0.64/0.72	[S](X) = 0
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	SCC Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length(X:S)) -> ACTIVE(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Strongly Connected Components:
0.64/0.72	->->Cycle:
0.64/0.72	->->-> Pairs:
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	->->-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	Reduction Pairs Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 ACTIVE(length1(X:S)) -> MARK(length(X:S))
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	-> Usable rules:
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	->Interpretation type:
0.64/0.72	 Linear
0.64/0.72	->Coefficients:
0.64/0.72	 Natural Numbers
0.64/0.72	->Dimension:
0.64/0.72	 1
0.64/0.72	->Bound:
0.64/0.72	 2
0.64/0.72	->Interpretation:
0.64/0.72	 
0.64/0.72	[active](X) = 2.X
0.64/0.72	[cons](X1,X2) = 0
0.64/0.72	[from](X) = 0
0.64/0.72	[length](X) = 2.X
0.64/0.72	[length1](X) = 2.X + 1
0.64/0.72	[mark](X) = 2.X
0.64/0.72	[s](X) = 2.X
0.64/0.72	[0] = 0
0.64/0.72	[fSNonEmpty] = 0
0.64/0.72	[nil] = 0
0.64/0.72	[ACTIVE](X) = X
0.64/0.72	[CONS](X1,X2) = 0
0.64/0.72	[FROM](X) = 0
0.64/0.72	[LENGTH](X) = 0
0.64/0.72	[LENGTH1](X) = 0
0.64/0.72	[MARK](X) = X
0.64/0.72	[S](X) = 0
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	SCC Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 MARK(length1(X:S)) -> ACTIVE(length1(X:S))
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Strongly Connected Components:
0.64/0.72	->->Cycle:
0.64/0.72	->->-> Pairs:
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	->->-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	Subterm Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 MARK(s(X:S)) -> MARK(X:S)
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Projection:
0.64/0.72	 pi(MARK) = 1
0.64/0.72	
0.64/0.72	Problem 1.6: 
0.64/0.72	
0.64/0.72	SCC Processor:
0.64/0.72	-> Pairs:
0.64/0.72	 Empty
0.64/0.72	-> Rules:
0.64/0.72	 active(from(X:S)) -> mark(cons(X:S,from(s(X:S))))
0.64/0.72	 active(length(cons(X:S,Y:S))) -> mark(s(length1(Y:S)))
0.64/0.72	 active(length(nil)) -> mark(0)
0.64/0.72	 active(length1(X:S)) -> mark(length(X:S))
0.64/0.72	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.72	 from(active(X:S)) -> from(X:S)
0.64/0.72	 from(mark(X:S)) -> from(X:S)
0.64/0.72	 length(active(X:S)) -> length(X:S)
0.64/0.72	 length(mark(X:S)) -> length(X:S)
0.64/0.72	 length1(active(X:S)) -> length1(X:S)
0.64/0.72	 length1(mark(X:S)) -> length1(X:S)
0.64/0.72	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.72	 mark(from(X:S)) -> active(from(mark(X:S)))
0.64/0.72	 mark(length(X:S)) -> active(length(X:S))
0.64/0.72	 mark(length1(X:S)) -> active(length1(X:S))
0.64/0.72	 mark(s(X:S)) -> active(s(mark(X:S)))
0.64/0.72	 mark(0) -> active(0)
0.64/0.72	 mark(nil) -> active(nil)
0.64/0.72	 s(active(X:S)) -> s(X:S)
0.64/0.72	 s(mark(X:S)) -> s(X:S)
0.64/0.72	->Strongly Connected Components:
0.64/0.72	 There is no strongly connected component
0.64/0.72	
0.64/0.72	The problem is finite.
0.64/0.72	EOF