YES

(VAR x0 x1 x y)
(RULES
  s(g(s(0()),x0)) -> g(s(0()),s(x0))
  g(s(0()),s(0())) -> s(0())
  g(s(0()),0()) -> 0()
  g(s(0()),s(g(x0,x1))) -> s(g(s(x0),x1))
  g(s(0()),g(x,y)) -> g(s(x),y)
  f(x0,0()) -> g(s(0()),x0)
  f(s(0()),x0) -> s(x0)
  h(0()) -> s(0())
  g(0(),y) -> y
  s(f(x,y)) -> f(s(x),y)
  f(0(),y) -> y
  s(s(x)) -> x
)

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

  s_A(x1) = x1 + 1
  f_A(x1,x2) = x1 + x2 + 1
  0_A = 1
  g_A(x1,x2) = x2 + 2
  h_A(x1) = 2
  f#_A(x1,x2) = x2
  0#_A = 0

weights

  w0 = 1
  w(s) = 1
  w(f) = 3
  w(0) = 1
  w(g) = 0
  w(h) = 2

and precedence:

h > s > f > g > 0
)