(VAR N X X1 X2 Y Z )
(RULES 
        active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N))))
        active(sqr(0)) -> mark(0)
        active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X))))
        active(dbl(0)) -> mark(0)
        active(dbl(s(X))) -> mark(s(s(dbl(X))))
        active(add(0, X)) -> mark(X)
        active(add(s(X), Y)) -> mark(s(add(X, Y)))
        active(first(0, X)) -> mark(nil)
        active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
        active(terms(X)) -> terms(active(X))
        active(cons(X1, X2)) -> cons(active(X1), X2)
        active(recip(X)) -> recip(active(X))
        active(sqr(X)) -> sqr(active(X))
        active(add(X1, X2)) -> add(active(X1), X2)
        active(add(X1, X2)) -> add(X1, active(X2))
        active(dbl(X)) -> dbl(active(X))
        active(first(X1, X2)) -> first(active(X1), X2)
        active(first(X1, X2)) -> first(X1, active(X2))
        terms(mark(X)) -> mark(terms(X))
        cons(mark(X1), X2) -> mark(cons(X1, X2))
        recip(mark(X)) -> mark(recip(X))
        sqr(mark(X)) -> mark(sqr(X))
        add(mark(X1), X2) -> mark(add(X1, X2))
        add(X1, mark(X2)) -> mark(add(X1, X2))
        dbl(mark(X)) -> mark(dbl(X))
        first(mark(X1), X2) -> mark(first(X1, X2))
        first(X1, mark(X2)) -> mark(first(X1, X2))
        proper(terms(X)) -> terms(proper(X))
        proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
        proper(recip(X)) -> recip(proper(X))
        proper(sqr(X)) -> sqr(proper(X))
        proper(s(X)) -> s(proper(X))
        proper(0) -> ok(0)
        proper(add(X1, X2)) -> add(proper(X1), proper(X2))
        proper(dbl(X)) -> dbl(proper(X))
        proper(first(X1, X2)) -> first(proper(X1), proper(X2))
        proper(nil) -> ok(nil)
        terms(ok(X)) -> ok(terms(X))
        cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
        recip(ok(X)) -> ok(recip(X))
        sqr(ok(X)) -> ok(sqr(X))
        s(ok(X)) -> ok(s(X))
        add(ok(X1), ok(X2)) -> ok(add(X1, X2))
        dbl(ok(X)) -> ok(dbl(X))
        first(ok(X1), ok(X2)) -> ok(first(X1, X2))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
        
)