(VAR X X1 X2 X3 Y Z )
(RULES 
        active(primes) -> mark(sieve(from(s(s(0)))))
        active(from(X)) -> mark(cons(X, from(s(X))))
        active(head(cons(X, Y))) -> mark(X)
        active(tail(cons(X, Y))) -> mark(Y)
        active(if(true, X, Y)) -> mark(X)
        active(if(false, X, Y)) -> mark(Y)
        active(filter(s(s(X)), cons(Y, Z))) -> mark(if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))))
        active(sieve(cons(X, Y))) -> mark(cons(X, filter(X, sieve(Y))))
        active(sieve(X)) -> sieve(active(X))
        active(from(X)) -> from(active(X))
        active(s(X)) -> s(active(X))
        active(cons(X1, X2)) -> cons(active(X1), X2)
        active(head(X)) -> head(active(X))
        active(tail(X)) -> tail(active(X))
        active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
        active(filter(X1, X2)) -> filter(active(X1), X2)
        active(filter(X1, X2)) -> filter(X1, active(X2))
        active(divides(X1, X2)) -> divides(active(X1), X2)
        active(divides(X1, X2)) -> divides(X1, active(X2))
        sieve(mark(X)) -> mark(sieve(X))
        from(mark(X)) -> mark(from(X))
        s(mark(X)) -> mark(s(X))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        head(mark(X)) -> mark(head(X))
        tail(mark(X)) -> mark(tail(X))
        if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
        filter(mark(X1), X2) -> mark(filter(X1, X2))
        filter(X1, mark(X2)) -> mark(filter(X1, X2))
        divides(mark(X1), X2) -> mark(divides(X1, X2))
        divides(X1, mark(X2)) -> mark(divides(X1, X2))
        proper(primes) -> ok(primes)
        proper(sieve(X)) -> sieve(proper(X))
        proper(from(X)) -> from(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(0) -> ok(0)
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(head(X)) -> head(proper(X))
        proper(tail(X)) -> tail(proper(X))
        proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
        proper(true) -> ok(true)
        proper(false) -> ok(false)
        proper(filter(X1, X2)) -> filter(proper(X1), proper(X2))
        proper(divides(X1, X2)) -> divides(proper(X1), proper(X2))
        sieve(ok(X)) -> ok(sieve(X))
        from(ok(X)) -> ok(from(X))
        s(ok(X)) -> ok(s(X))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        head(ok(X)) -> ok(head(X))
        tail(ok(X)) -> ok(tail(X))
        if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
        filter(ok(X1), ok(X2)) -> ok(filter(X1, X2))
        divides(ok(X1), ok(X2)) -> ok(divides(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)