(VAR X X1 X2 X3 Y Z )
(RULES 
        a__primes -> a__sieve(a__from(s(s(0))))
        a__from(X) -> cons(mark(X), from(s(X)))
        a__head(cons(X, Y)) -> mark(X)
        a__tail(cons(X, Y)) -> mark(Y)
        a__if(true, X, Y) -> mark(X)
        a__if(false, X, Y) -> mark(Y)
        a__filter(s(s(X)), cons(Y, Z)) -> a__if(divides(s(s(mark(X))), mark(Y)), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y))))
        a__sieve(cons(X, Y)) -> cons(mark(X), filter(X, sieve(Y)))
        mark(primes) -> a__primes
        mark(sieve(X)) -> a__sieve(mark(X))
        mark(from(X)) -> a__from(mark(X))
        mark(head(X)) -> a__head(mark(X))
        mark(tail(X)) -> a__tail(mark(X))
        mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
        mark(filter(X1, X2)) -> a__filter(mark(X1), mark(X2))
        mark(s(X)) -> s(mark(X))
        mark(0) -> 0
        mark(cons(X1, X2)) -> cons(mark(X1), X2)
        mark(true) -> true
        mark(false) -> false
        mark(divides(X1, X2)) -> divides(mark(X1), mark(X2))
        a__primes -> primes
        a__sieve(X) -> sieve(X)
        a__from(X) -> from(X)
        a__head(X) -> head(X)
        a__tail(X) -> tail(X)
        a__if(X1, X2, X3) -> if(X1, X2, X3)
        a__filter(X1, X2) -> filter(X1, X2)
        
)