(VAR N X X1 X2 Y Z )
(RULES 
        a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
        a__sqr(0) -> 0
        a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
        a__dbl(0) -> 0
        a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
        a__add(0, X) -> mark(X)
        a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
        a__first(0, X) -> nil
        a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
        a__half(0) -> 0
        a__half(s(0)) -> 0
        a__half(s(s(X))) -> s(a__half(mark(X)))
        a__half(dbl(X)) -> mark(X)
        mark(terms(X)) -> a__terms(mark(X))
        mark(sqr(X)) -> a__sqr(mark(X))
        mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
        mark(dbl(X)) -> a__dbl(mark(X))
        mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
        mark(half(X)) -> a__half(mark(X))
        mark(cons(X1, X2)) -> cons(mark(X1), X2)
        mark(recip(X)) -> recip(mark(X))
        mark(s(X)) -> s(mark(X))
        mark(0) -> 0
        mark(nil) -> nil
        a__terms(X) -> terms(X)
        a__sqr(X) -> sqr(X)
        a__add(X1, X2) -> add(X1, X2)
        a__dbl(X) -> dbl(X)
        a__first(X1, X2) -> first(X1, X2)
        a__half(X) -> half(X)
        
)