YES

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

(COMMENT
Termination is shown by ELPO with interpretations on natural numbers

  p_A(x1,x2) = x1
  0_A = 0
  s_A(x1) = x1
  f_A(x1) = 1
  g_A(x1) = 39946
  b_A(x1,x2) = x1 + 39945
  n_A(x1) = x1 + 39947
  u_A(x1) = x1 + 1
  0#_A = 0
  f#_A(x1) = 0
  g#_A(x1) = x1

and precedence:

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