YES

(VAR x y z)
(RULES
  g(x) -> b(f(s(x)),f(x))
  u(b(x,0())) -> x
  u(b(x,s(y))) -> s(u(b(x,y)))
  f(s(s(z))) -> u(b(f(s(z)),f(z)))
  p(x,y) -> u(b(x,y))
  n(b(x,y)) -> b(u(b(x,y)),x)
  f(s(0())) -> s(0())
  f(0()) -> 0()
)

(COMMENT
Termination is shown by LPO with precedence:

  n > p > g > f > u > b > s > 0
)