MAYBE

Problem:
 terms(N) -> cons(recip(sqr(N)),n__terms(s(N)))
 sqr(0()) -> 0()
 sqr(s(X)) -> s(add(sqr(X),dbl(X)))
 dbl(0()) -> 0()
 dbl(s(X)) -> s(s(dbl(X)))
 add(0(),X) -> X
 add(s(X),Y) -> s(add(X,Y))
 first(0(),X) -> nil()
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(X))) -> s(half(X))
 half(dbl(X)) -> X
 terms(X) -> n__terms(X)
 first(X1,X2) -> n__first(X1,X2)
 activate(n__terms(X)) -> terms(X)
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(X) -> X

Proof:
 Open