YES

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

(COMMENT
Termination is shown by KBO with weight

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

and precedence:

  g > h > f > s > 0
)