MAYBE

Problem:
 tower(x) -> f(a(),x,s(0()))
 f(a(),0(),y) -> y
 f(a(),s(x),y) -> f(b(),y,s(x))
 f(b(),y,x) -> f(a(),half(x),exp(y))
 exp(0()) -> s(0())
 exp(s(x)) -> double(exp(x))
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 half(0()) -> double(0())
 half(s(0())) -> half(0())
 half(s(s(x))) -> s(half(x))

Proof:
 Open