0.64/0.73	YES
0.64/0.73	
0.64/0.73	Problem 1: 
0.64/0.73	
0.64/0.73	(VAR v_NonEmpty:S N:S X:S X1:S X2:S Y:S Z:S)
0.64/0.73	(RULES
0.64/0.73	active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.73	active(add(0,X:S)) -> mark(X:S)
0.64/0.73	active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.73	active(dbl(0)) -> mark(0)
0.64/0.73	active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.73	active(first(0,X:S)) -> mark(nil)
0.64/0.73	active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.73	active(sqr(0)) -> mark(0)
0.64/0.73	active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.73	add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.73	add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.73	add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.73	add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.73	cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.73	cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.73	cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.73	cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.73	dbl(active(X:S)) -> dbl(X:S)
0.64/0.73	dbl(mark(X:S)) -> dbl(X:S)
0.64/0.73	first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.73	first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.73	first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.73	first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.73	mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.73	mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.73	mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.73	mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.73	mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.73	mark(s(X:S)) -> active(s(X:S))
0.64/0.73	mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.73	mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.73	mark(0) -> active(0)
0.64/0.73	mark(nil) -> active(nil)
0.64/0.73	recip(active(X:S)) -> recip(X:S)
0.64/0.73	recip(mark(X:S)) -> recip(X:S)
0.64/0.73	s(active(X:S)) -> s(X:S)
0.64/0.73	s(mark(X:S)) -> s(X:S)
0.64/0.73	sqr(active(X:S)) -> sqr(X:S)
0.64/0.73	sqr(mark(X:S)) -> sqr(X:S)
0.64/0.73	terms(active(X:S)) -> terms(X:S)
0.64/0.73	terms(mark(X:S)) -> terms(X:S)
0.64/0.73	) 
0.64/0.73	(STRATEGY INNERMOST)
0.64/0.73	
0.64/0.73	Problem 1: 
0.64/0.73	
0.64/0.73	Dependency Pairs Processor:
0.64/0.73	-> Pairs:
0.64/0.73	 ACTIVE(add(s(X:S),Y:S)) -> ADD(X:S,Y:S)
0.64/0.73	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.64/0.73	 ACTIVE(add(s(X:S),Y:S)) -> S(add(X:S,Y:S))
0.64/0.73	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.73	 ACTIVE(dbl(s(X:S))) -> DBL(X:S)
0.64/0.73	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.73	 ACTIVE(dbl(s(X:S))) -> S(dbl(X:S))
0.64/0.73	 ACTIVE(dbl(s(X:S))) -> S(s(dbl(X:S)))
0.64/0.74	 ACTIVE(dbl(0)) -> MARK(0)
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> CONS(Y:S,first(X:S,Z:S))
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> FIRST(X:S,Z:S)
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 ACTIVE(first(0,X:S)) -> MARK(nil)
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> ADD(sqr(X:S),dbl(X:S))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> DBL(X:S)
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> S(add(sqr(X:S),dbl(X:S)))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> SQR(X:S)
0.64/0.74	 ACTIVE(sqr(0)) -> MARK(0)
0.64/0.74	 ACTIVE(terms(N:S)) -> CONS(recip(sqr(N:S)),terms(s(N:S)))
0.64/0.74	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 ACTIVE(terms(N:S)) -> RECIP(sqr(N:S))
0.64/0.74	 ACTIVE(terms(N:S)) -> S(N:S)
0.64/0.74	 ACTIVE(terms(N:S)) -> SQR(N:S)
0.64/0.74	 ACTIVE(terms(N:S)) -> TERMS(s(N:S))
0.64/0.74	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 DBL(active(X:S)) -> DBL(X:S)
0.64/0.74	 DBL(mark(X:S)) -> DBL(X:S)
0.64/0.74	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> ADD(mark(X1:S),mark(X2:S))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.74	 MARK(dbl(X:S)) -> DBL(mark(X:S))
0.64/0.74	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(first(X1:S,X2:S)) -> FIRST(mark(X1:S),mark(X2:S))
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.74	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(recip(X:S)) -> RECIP(mark(X:S))
0.64/0.74	 MARK(s(X:S)) -> ACTIVE(s(X:S))
0.64/0.74	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.74	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(sqr(X:S)) -> SQR(mark(X:S))
0.64/0.74	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.74	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(terms(X:S)) -> TERMS(mark(X:S))
0.64/0.74	 RECIP(active(X:S)) -> RECIP(X:S)
0.64/0.74	 RECIP(mark(X:S)) -> RECIP(X:S)
0.64/0.74	 S(active(X:S)) -> S(X:S)
0.64/0.74	 S(mark(X:S)) -> S(X:S)
0.64/0.74	 SQR(active(X:S)) -> SQR(X:S)
0.64/0.74	 SQR(mark(X:S)) -> SQR(X:S)
0.64/0.74	 TERMS(active(X:S)) -> TERMS(X:S)
0.64/0.74	 TERMS(mark(X:S)) -> TERMS(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	
0.64/0.74	Problem 1: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 ACTIVE(add(s(X:S),Y:S)) -> ADD(X:S,Y:S)
0.64/0.74	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.64/0.74	 ACTIVE(add(s(X:S),Y:S)) -> S(add(X:S,Y:S))
0.64/0.74	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.74	 ACTIVE(dbl(s(X:S))) -> DBL(X:S)
0.64/0.74	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.74	 ACTIVE(dbl(s(X:S))) -> S(dbl(X:S))
0.64/0.74	 ACTIVE(dbl(s(X:S))) -> S(s(dbl(X:S)))
0.64/0.74	 ACTIVE(dbl(0)) -> MARK(0)
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> CONS(Y:S,first(X:S,Z:S))
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> FIRST(X:S,Z:S)
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 ACTIVE(first(0,X:S)) -> MARK(nil)
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> ADD(sqr(X:S),dbl(X:S))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> DBL(X:S)
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> S(add(sqr(X:S),dbl(X:S)))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> SQR(X:S)
0.64/0.74	 ACTIVE(sqr(0)) -> MARK(0)
0.64/0.74	 ACTIVE(terms(N:S)) -> CONS(recip(sqr(N:S)),terms(s(N:S)))
0.64/0.74	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 ACTIVE(terms(N:S)) -> RECIP(sqr(N:S))
0.64/0.74	 ACTIVE(terms(N:S)) -> S(N:S)
0.64/0.74	 ACTIVE(terms(N:S)) -> SQR(N:S)
0.64/0.74	 ACTIVE(terms(N:S)) -> TERMS(s(N:S))
0.64/0.74	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 DBL(active(X:S)) -> DBL(X:S)
0.64/0.74	 DBL(mark(X:S)) -> DBL(X:S)
0.64/0.74	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> ADD(mark(X1:S),mark(X2:S))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> CONS(mark(X1:S),X2:S)
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.74	 MARK(dbl(X:S)) -> DBL(mark(X:S))
0.64/0.74	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(first(X1:S,X2:S)) -> FIRST(mark(X1:S),mark(X2:S))
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.74	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(recip(X:S)) -> RECIP(mark(X:S))
0.64/0.74	 MARK(s(X:S)) -> ACTIVE(s(X:S))
0.64/0.74	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.74	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(sqr(X:S)) -> SQR(mark(X:S))
0.64/0.74	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.74	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(terms(X:S)) -> TERMS(mark(X:S))
0.64/0.74	 RECIP(active(X:S)) -> RECIP(X:S)
0.64/0.74	 RECIP(mark(X:S)) -> RECIP(X:S)
0.64/0.74	 S(active(X:S)) -> S(X:S)
0.64/0.74	 S(mark(X:S)) -> S(X:S)
0.64/0.74	 SQR(active(X:S)) -> SQR(X:S)
0.64/0.74	 SQR(mark(X:S)) -> SQR(X:S)
0.64/0.74	 TERMS(active(X:S)) -> TERMS(X:S)
0.64/0.74	 TERMS(mark(X:S)) -> TERMS(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 TERMS(active(X:S)) -> TERMS(X:S)
0.64/0.74	 TERMS(mark(X:S)) -> TERMS(X:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 SQR(active(X:S)) -> SQR(X:S)
0.64/0.74	 SQR(mark(X:S)) -> SQR(X:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 S(active(X:S)) -> S(X:S)
0.64/0.74	 S(mark(X:S)) -> S(X:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 RECIP(active(X:S)) -> RECIP(X:S)
0.64/0.74	 RECIP(mark(X:S)) -> RECIP(X:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 DBL(active(X:S)) -> DBL(X:S)
0.64/0.74	 DBL(mark(X:S)) -> DBL(X:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.64/0.74	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.74	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.74	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.74	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.74	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.74	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	
0.64/0.74	
0.64/0.74	The problem is decomposed in 9 subproblems.
0.64/0.74	
0.64/0.74	Problem 1.1: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 TERMS(active(X:S)) -> TERMS(X:S)
0.64/0.74	 TERMS(mark(X:S)) -> TERMS(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(TERMS) = 1
0.64/0.74	
0.64/0.74	Problem 1.1: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.2: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 SQR(active(X:S)) -> SQR(X:S)
0.64/0.74	 SQR(mark(X:S)) -> SQR(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(SQR) = 1
0.64/0.74	
0.64/0.74	Problem 1.2: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.3: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 S(active(X:S)) -> S(X:S)
0.64/0.74	 S(mark(X:S)) -> S(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(S) = 1
0.64/0.74	
0.64/0.74	Problem 1.3: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.4: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 RECIP(active(X:S)) -> RECIP(X:S)
0.64/0.74	 RECIP(mark(X:S)) -> RECIP(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(RECIP) = 1
0.64/0.74	
0.64/0.74	Problem 1.4: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.5: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 FIRST(active(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(mark(X1:S),X2:S) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(FIRST) = 1
0.64/0.74	
0.64/0.74	Problem 1.5: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	
0.64/0.74	Problem 1.5: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 FIRST(X1:S,active(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	 FIRST(X1:S,mark(X2:S)) -> FIRST(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(FIRST) = 2
0.64/0.74	
0.64/0.74	Problem 1.5: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.6: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 DBL(active(X:S)) -> DBL(X:S)
0.64/0.74	 DBL(mark(X:S)) -> DBL(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(DBL) = 1
0.64/0.74	
0.64/0.74	Problem 1.6: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.7: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 CONS(active(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(mark(X1:S),X2:S) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(CONS) = 1
0.64/0.74	
0.64/0.74	Problem 1.7: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	
0.64/0.74	Problem 1.7: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 CONS(X1:S,active(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	 CONS(X1:S,mark(X2:S)) -> CONS(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(CONS) = 2
0.64/0.74	
0.64/0.74	Problem 1.7: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.8: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 ADD(active(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(mark(X1:S),X2:S) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(ADD) = 1
0.64/0.74	
0.64/0.74	Problem 1.8: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	->->Cycle:
0.64/0.74	->->-> Pairs:
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	->->-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	
0.64/0.74	Problem 1.8: 
0.64/0.74	
0.64/0.74	Subterm Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 ADD(X1:S,active(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	 ADD(X1:S,mark(X2:S)) -> ADD(X1:S,X2:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Projection:
0.64/0.74	 pi(ADD) = 2
0.64/0.74	
0.64/0.74	Problem 1.8: 
0.64/0.74	
0.64/0.74	SCC Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 Empty
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	->Strongly Connected Components:
0.64/0.74	 There is no strongly connected component
0.64/0.74	
0.64/0.74	The problem is finite.
0.64/0.74	
0.64/0.74	Problem 1.9: 
0.64/0.74	
0.64/0.74	Reduction Pairs Processor:
0.64/0.74	-> Pairs:
0.64/0.74	 ACTIVE(add(s(X:S),Y:S)) -> MARK(s(add(X:S,Y:S)))
0.64/0.74	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.74	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.74	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.74	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.74	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.74	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.74	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.74	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.74	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.74	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.74	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.74	-> Rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.74	 recip(mark(X:S)) -> recip(X:S)
0.64/0.74	 s(active(X:S)) -> s(X:S)
0.64/0.74	 s(mark(X:S)) -> s(X:S)
0.64/0.74	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.74	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.74	 terms(active(X:S)) -> terms(X:S)
0.64/0.74	 terms(mark(X:S)) -> terms(X:S)
0.64/0.74	-> Usable rules:
0.64/0.74	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.74	 active(add(0,X:S)) -> mark(X:S)
0.64/0.74	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.74	 active(dbl(0)) -> mark(0)
0.64/0.74	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.74	 active(first(0,X:S)) -> mark(nil)
0.64/0.74	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.74	 active(sqr(0)) -> mark(0)
0.64/0.74	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.74	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.74	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.74	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.74	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.74	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.74	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.74	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.74	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.74	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.74	 mark(s(X:S)) -> active(s(X:S))
0.64/0.74	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.74	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.74	 mark(0) -> active(0)
0.64/0.74	 mark(nil) -> active(nil)
0.64/0.74	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[active](X) = X
0.64/0.75	[add](X1,X2) = 2.X1 + 2.X2 + 1
0.64/0.75	[cons](X1,X2) = X1
0.64/0.75	[dbl](X) = 2.X + 2
0.64/0.75	[first](X1,X2) = 2.X1 + 2.X2
0.64/0.75	[mark](X) = 2.X
0.64/0.75	[recip](X) = X
0.64/0.75	[s](X) = 1
0.64/0.75	[sqr](X) = X + 1
0.64/0.75	[terms](X) = 2.X + 2
0.64/0.75	[0] = 0
0.64/0.75	[fSNonEmpty] = 0
0.64/0.75	[nil] = 0
0.64/0.75	[ACTIVE](X) = X + 2
0.64/0.75	[ADD](X1,X2) = 0
0.64/0.75	[CONS](X1,X2) = 0
0.64/0.75	[DBL](X) = 0
0.64/0.75	[FIRST](X1,X2) = 0
0.64/0.75	[MARK](X) = 2.X + 2
0.64/0.75	[RECIP](X) = 0
0.64/0.75	[S](X) = 0
0.64/0.75	[SQR](X) = 0
0.64/0.75	[TERMS](X) = 0
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.75	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.75	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	Reduction Pairs Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(add(0,X:S)) -> MARK(X:S)
0.64/0.75	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	-> Usable rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[active](X) = X
0.64/0.75	[add](X1,X2) = 2.X1 + 2.X2 + 2
0.64/0.75	[cons](X1,X2) = X1
0.64/0.75	[dbl](X) = X + 1
0.64/0.75	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.64/0.75	[mark](X) = 2.X
0.64/0.75	[recip](X) = X
0.64/0.75	[s](X) = 1
0.64/0.75	[sqr](X) = X + 1
0.64/0.75	[terms](X) = 2.X + 2
0.64/0.75	[0] = 0
0.64/0.75	[fSNonEmpty] = 0
0.64/0.75	[nil] = 1
0.64/0.75	[ACTIVE](X) = X + 2
0.64/0.75	[ADD](X1,X2) = 0
0.64/0.75	[CONS](X1,X2) = 0
0.64/0.75	[DBL](X) = 0
0.64/0.75	[FIRST](X1,X2) = 0
0.64/0.75	[MARK](X) = 2.X + 2
0.64/0.75	[RECIP](X) = 0
0.64/0.75	[S](X) = 0
0.64/0.75	[SQR](X) = 0
0.64/0.75	[TERMS](X) = 0
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	Reduction Pairs Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(dbl(s(X:S))) -> MARK(s(s(dbl(X:S))))
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	-> Usable rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[active](X) = X
0.64/0.75	[add](X1,X2) = X1 + 2.X2
0.64/0.75	[cons](X1,X2) = X1
0.64/0.75	[dbl](X) = 2.X + 2
0.64/0.75	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.64/0.75	[mark](X) = 2.X
0.64/0.75	[recip](X) = X
0.64/0.75	[s](X) = 0
0.64/0.75	[sqr](X) = X + 1
0.64/0.75	[terms](X) = 2.X + 2
0.64/0.75	[0] = 1
0.64/0.75	[fSNonEmpty] = 0
0.64/0.75	[nil] = 2
0.64/0.75	[ACTIVE](X) = X + 2
0.64/0.75	[ADD](X1,X2) = 0
0.64/0.75	[CONS](X1,X2) = 0
0.64/0.75	[DBL](X) = 0
0.64/0.75	[FIRST](X1,X2) = 0
0.64/0.75	[MARK](X) = 2.X + 2
0.64/0.75	[RECIP](X) = 0
0.64/0.75	[S](X) = 0
0.64/0.75	[SQR](X) = 0
0.64/0.75	[TERMS](X) = 0
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	Reduction Pairs Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(first(s(X:S),cons(Y:S,Z:S))) -> MARK(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	-> Usable rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[active](X) = X
0.64/0.75	[add](X1,X2) = X1 + 2.X2 + 2
0.64/0.75	[cons](X1,X2) = X1
0.64/0.75	[dbl](X) = 2.X + 1
0.64/0.75	[first](X1,X2) = 2.X1 + 2.X2 + 2
0.64/0.75	[mark](X) = 2.X
0.64/0.75	[recip](X) = X + 1
0.64/0.75	[s](X) = 0
0.64/0.75	[sqr](X) = X
0.64/0.75	[terms](X) = 2.X + 2
0.64/0.75	[0] = 0
0.64/0.75	[fSNonEmpty] = 0
0.64/0.75	[nil] = 1
0.64/0.75	[ACTIVE](X) = X + 1
0.64/0.75	[ADD](X1,X2) = 0
0.64/0.75	[CONS](X1,X2) = 0
0.64/0.75	[DBL](X) = 0
0.64/0.75	[FIRST](X1,X2) = 0
0.64/0.75	[MARK](X) = 2.X + 1
0.64/0.75	[RECIP](X) = 0
0.64/0.75	[S](X) = 0
0.64/0.75	[SQR](X) = 0
0.64/0.75	[TERMS](X) = 0
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	Reduction Pairs Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(sqr(s(X:S))) -> MARK(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	-> Usable rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[active](X) = X
0.64/0.75	[add](X1,X2) = X1 + 2.X2 + 2
0.64/0.75	[cons](X1,X2) = X1
0.64/0.75	[dbl](X) = 2.X + 2
0.64/0.75	[first](X1,X2) = 2.X1 + 2.X2
0.64/0.75	[mark](X) = 2.X
0.64/0.75	[recip](X) = X
0.64/0.75	[s](X) = 0
0.64/0.75	[sqr](X) = X + 1
0.64/0.75	[terms](X) = 2.X + 2
0.64/0.75	[0] = 0
0.64/0.75	[fSNonEmpty] = 0
0.64/0.75	[nil] = 0
0.64/0.75	[ACTIVE](X) = X + 2
0.64/0.75	[ADD](X1,X2) = 0
0.64/0.75	[CONS](X1,X2) = 0
0.64/0.75	[DBL](X) = 0
0.64/0.75	[FIRST](X1,X2) = 0
0.64/0.75	[MARK](X) = 2.X + 2
0.64/0.75	[RECIP](X) = 0
0.64/0.75	[S](X) = 0
0.64/0.75	[SQR](X) = 0
0.64/0.75	[TERMS](X) = 0
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	Reduction Pairs Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 ACTIVE(terms(N:S)) -> MARK(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	-> Usable rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[active](X) = X
0.64/0.75	[add](X1,X2) = X1 + 2.X2 + 2
0.64/0.75	[cons](X1,X2) = X1
0.64/0.75	[dbl](X) = 2.X + 2
0.64/0.75	[first](X1,X2) = 2.X1 + 2.X2 + 1
0.64/0.75	[mark](X) = 2.X
0.64/0.75	[recip](X) = X
0.64/0.75	[s](X) = 0
0.64/0.75	[sqr](X) = X
0.64/0.75	[terms](X) = 2.X + 2
0.64/0.75	[0] = 0
0.64/0.75	[fSNonEmpty] = 0
0.64/0.75	[nil] = 0
0.64/0.75	[ACTIVE](X) = X + 2
0.64/0.75	[ADD](X1,X2) = 0
0.64/0.75	[CONS](X1,X2) = 0
0.64/0.75	[DBL](X) = 0
0.64/0.75	[FIRST](X1,X2) = 0
0.64/0.75	[MARK](X) = 2.X + 2
0.64/0.75	[RECIP](X) = 0
0.64/0.75	[S](X) = 0
0.64/0.75	[SQR](X) = 0
0.64/0.75	[TERMS](X) = 0
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 MARK(add(X1:S,X2:S)) -> ACTIVE(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> ACTIVE(cons(mark(X1:S),X2:S))
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> ACTIVE(dbl(mark(X:S)))
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> ACTIVE(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> ACTIVE(recip(mark(X:S)))
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> ACTIVE(sqr(mark(X:S)))
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> ACTIVE(terms(mark(X:S)))
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	Subterm Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(add(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(dbl(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X1:S)
0.64/0.75	 MARK(first(X1:S,X2:S)) -> MARK(X2:S)
0.64/0.75	 MARK(recip(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(sqr(X:S)) -> MARK(X:S)
0.64/0.75	 MARK(terms(X:S)) -> MARK(X:S)
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Projection:
0.64/0.75	 pi(MARK) = 1
0.64/0.75	
0.64/0.75	Problem 1.9: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 Empty
0.64/0.75	-> Rules:
0.64/0.75	 active(add(s(X:S),Y:S)) -> mark(s(add(X:S,Y:S)))
0.64/0.75	 active(add(0,X:S)) -> mark(X:S)
0.64/0.75	 active(dbl(s(X:S))) -> mark(s(s(dbl(X:S))))
0.64/0.75	 active(dbl(0)) -> mark(0)
0.64/0.75	 active(first(s(X:S),cons(Y:S,Z:S))) -> mark(cons(Y:S,first(X:S,Z:S)))
0.64/0.75	 active(first(0,X:S)) -> mark(nil)
0.64/0.75	 active(sqr(s(X:S))) -> mark(s(add(sqr(X:S),dbl(X:S))))
0.64/0.75	 active(sqr(0)) -> mark(0)
0.64/0.75	 active(terms(N:S)) -> mark(cons(recip(sqr(N:S)),terms(s(N:S))))
0.64/0.75	 add(active(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(mark(X1:S),X2:S) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,active(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 add(X1:S,mark(X2:S)) -> add(X1:S,X2:S)
0.64/0.75	 cons(active(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(mark(X1:S),X2:S) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,active(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 cons(X1:S,mark(X2:S)) -> cons(X1:S,X2:S)
0.64/0.75	 dbl(active(X:S)) -> dbl(X:S)
0.64/0.75	 dbl(mark(X:S)) -> dbl(X:S)
0.64/0.75	 first(active(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(mark(X1:S),X2:S) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,active(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 first(X1:S,mark(X2:S)) -> first(X1:S,X2:S)
0.64/0.75	 mark(add(X1:S,X2:S)) -> active(add(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(cons(X1:S,X2:S)) -> active(cons(mark(X1:S),X2:S))
0.64/0.75	 mark(dbl(X:S)) -> active(dbl(mark(X:S)))
0.64/0.75	 mark(first(X1:S,X2:S)) -> active(first(mark(X1:S),mark(X2:S)))
0.64/0.75	 mark(recip(X:S)) -> active(recip(mark(X:S)))
0.64/0.75	 mark(s(X:S)) -> active(s(X:S))
0.64/0.75	 mark(sqr(X:S)) -> active(sqr(mark(X:S)))
0.64/0.75	 mark(terms(X:S)) -> active(terms(mark(X:S)))
0.64/0.75	 mark(0) -> active(0)
0.64/0.75	 mark(nil) -> active(nil)
0.64/0.75	 recip(active(X:S)) -> recip(X:S)
0.64/0.75	 recip(mark(X:S)) -> recip(X:S)
0.64/0.75	 s(active(X:S)) -> s(X:S)
0.64/0.75	 s(mark(X:S)) -> s(X:S)
0.64/0.75	 sqr(active(X:S)) -> sqr(X:S)
0.64/0.75	 sqr(mark(X:S)) -> sqr(X:S)
0.64/0.75	 terms(active(X:S)) -> terms(X:S)
0.64/0.75	 terms(mark(X:S)) -> terms(X:S)
0.64/0.75	->Strongly Connected Components:
0.64/0.75	 There is no strongly connected component
0.64/0.75	
0.64/0.75	The problem is finite.
0.64/0.75	EOF