0.00/0.18	YES
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	(VAR v_NonEmpty:S M:S N:S X:S X1:S X2:S X3:S Y:S)
0.00/0.18	(RULES
0.00/0.18	a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	a__nats(X:S) -> nats(X:S)
0.00/0.18	a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	a__sieve(X:S) -> sieve(X:S)
0.00/0.18	a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	a__zprimes -> zprimes
0.00/0.18	mark(0) -> 0
0.00/0.18	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	mark(zprimes) -> a__zprimes
0.00/0.18	) 
0.00/0.18	(STRATEGY INNERMOST)
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Dependency Pairs Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__FILTER(cons(X:S,Y:S),s(N:S),M:S) -> MARK(X:S)
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> A__FILTER(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__FILTER(cons(X:S,Y:S),s(N:S),M:S) -> MARK(X:S)
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> A__FILTER(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 A__FILTER(cons(X:S,Y:S),s(N:S),M:S) -> MARK(X:S)
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> A__FILTER(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	->->-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__FILTER(cons(X:S,Y:S),s(N:S),M:S) -> MARK(X:S)
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> A__FILTER(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	-> Usable rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a__filter](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.18	[a__nats](X) = 2.X + 1
0.00/0.18	[a__sieve](X) = 2.X
0.00/0.18	[a__zprimes] = 2
0.00/0.18	[mark](X) = 2.X
0.00/0.18	[0] = 0
0.00/0.18	[cons](X1,X2) = X1 + 1
0.00/0.18	[fSNonEmpty] = 0
0.00/0.18	[filter](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 1
0.00/0.18	[nats](X) = 2.X + 1
0.00/0.18	[s](X) = 2.X
0.00/0.18	[sieve](X) = 2.X
0.00/0.18	[zprimes] = 1
0.00/0.18	[A__FILTER](X1,X2,X3) = 2.X1 + 2.X3 + 2
0.00/0.18	[A__NATS](X) = 2.X + 2
0.00/0.18	[A__SIEVE](X) = 2.X
0.00/0.18	[A__ZPRIMES] = 2
0.00/0.18	[MARK](X) = 2.X + 2
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> A__FILTER(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	->->-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__NATS(N:S) -> MARK(N:S)
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	-> Usable rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a__filter](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.18	[a__nats](X) = 2.X + 2
0.00/0.18	[a__sieve](X) = X
0.00/0.18	[a__zprimes] = 2
0.00/0.18	[mark](X) = X
0.00/0.18	[0] = 0
0.00/0.18	[cons](X1,X2) = 2.X1 + 2
0.00/0.18	[fSNonEmpty] = 0
0.00/0.18	[filter](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2
0.00/0.18	[nats](X) = 2.X + 2
0.00/0.18	[s](X) = 2.X
0.00/0.18	[sieve](X) = X
0.00/0.18	[zprimes] = 2
0.00/0.18	[A__FILTER](X1,X2,X3) = 0
0.00/0.18	[A__NATS](X) = 2.X + 2
0.00/0.18	[A__SIEVE](X) = X
0.00/0.18	[A__ZPRIMES] = 2
0.00/0.18	[MARK](X) = 2.X + 1
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__NATS(s(s(0)))
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> A__NATS(mark(X:S))
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	->->-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Reduction Pairs Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__SIEVE(cons(s(N:S),Y:S)) -> MARK(N:S)
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	-> Usable rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Interpretation type:
0.00/0.18	 Linear
0.00/0.18	->Coefficients:
0.00/0.18	 Natural Numbers
0.00/0.18	->Dimension:
0.00/0.18	 1
0.00/0.18	->Bound:
0.00/0.18	 2
0.00/0.18	->Interpretation:
0.00/0.18	 
0.00/0.18	[a__filter](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2
0.00/0.18	[a__nats](X) = 2.X
0.00/0.18	[a__sieve](X) = 2.X + 2
0.00/0.18	[a__zprimes] = 2
0.00/0.18	[mark](X) = 2.X
0.00/0.18	[0] = 0
0.00/0.18	[cons](X1,X2) = X1
0.00/0.18	[fSNonEmpty] = 0
0.00/0.18	[filter](X1,X2,X3) = 2.X1 + 2.X2 + X3 + 2
0.00/0.18	[nats](X) = 2.X
0.00/0.18	[s](X) = 2.X
0.00/0.18	[sieve](X) = 2.X + 2
0.00/0.18	[zprimes] = 2
0.00/0.18	[A__FILTER](X1,X2,X3) = 0
0.00/0.18	[A__NATS](X) = 0
0.00/0.18	[A__SIEVE](X) = 2.X + 1
0.00/0.18	[A__ZPRIMES] = 2
0.00/0.18	[MARK](X) = 2.X
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 A__ZPRIMES -> A__SIEVE(a__nats(s(s(0))))
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> A__SIEVE(mark(X:S))
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(zprimes) -> A__ZPRIMES
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Strongly Connected Components:
0.00/0.18	->->Cycle:
0.00/0.18	->->-> Pairs:
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	->->-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	Subterm Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X1:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X2:S)
0.00/0.18	 MARK(filter(X1:S,X2:S,X3:S)) -> MARK(X3:S)
0.00/0.18	 MARK(nats(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(s(X:S)) -> MARK(X:S)
0.00/0.18	 MARK(sieve(X:S)) -> MARK(X:S)
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Projection:
0.00/0.18	 pi(MARK) = 1
0.00/0.18	
0.00/0.18	Problem 1: 
0.00/0.18	
0.00/0.18	SCC Processor:
0.00/0.18	-> Pairs:
0.00/0.18	 Empty
0.00/0.18	-> Rules:
0.00/0.18	 a__filter(cons(X:S,Y:S),0,M:S) -> cons(0,filter(Y:S,M:S,M:S))
0.00/0.18	 a__filter(cons(X:S,Y:S),s(N:S),M:S) -> cons(mark(X:S),filter(Y:S,N:S,M:S))
0.00/0.18	 a__filter(X1:S,X2:S,X3:S) -> filter(X1:S,X2:S,X3:S)
0.00/0.18	 a__nats(N:S) -> cons(mark(N:S),nats(s(N:S)))
0.00/0.18	 a__nats(X:S) -> nats(X:S)
0.00/0.18	 a__sieve(cons(0,Y:S)) -> cons(0,sieve(Y:S))
0.00/0.18	 a__sieve(cons(s(N:S),Y:S)) -> cons(s(mark(N:S)),sieve(filter(Y:S,N:S,N:S)))
0.00/0.18	 a__sieve(X:S) -> sieve(X:S)
0.00/0.18	 a__zprimes -> a__sieve(a__nats(s(s(0))))
0.00/0.18	 a__zprimes -> zprimes
0.00/0.18	 mark(0) -> 0
0.00/0.18	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
0.00/0.18	 mark(filter(X1:S,X2:S,X3:S)) -> a__filter(mark(X1:S),mark(X2:S),mark(X3:S))
0.00/0.18	 mark(nats(X:S)) -> a__nats(mark(X:S))
0.00/0.18	 mark(s(X:S)) -> s(mark(X:S))
0.00/0.18	 mark(sieve(X:S)) -> a__sieve(mark(X:S))
0.00/0.18	 mark(zprimes) -> a__zprimes
0.00/0.18	->Strongly Connected Components:
0.00/0.18	 There is no strongly connected component
0.00/0.18	
0.00/0.18	The problem is finite.
0.00/0.18	EOF