MAYBE

Problem:
 log(s(x1)) -> s(log(half(s(x1))))
 half(0(x1)) -> 0(s(s(half(x1))))
 half(s(0(x1))) -> 0(x1)
 half(s(s(x1))) -> s(half(p(s(s(x1)))))
 half(half(s(s(s(s(x1)))))) -> s(s(half(half(x1))))
 p(s(s(s(x1)))) -> s(p(s(s(x1))))
 s(s(p(s(x1)))) -> s(s(x1))
 0(x1) -> x1

Proof:
 Open