YES

   1: f(g(x1)) -> h(g(x1),g(x1))
   2: f(s(x1)) -> h(s(x1),s(x1))
   3: g(x1) -> s(x1)

@Rule Labeling
--- R
   1: f(g(x1)) -> h(g(x1),g(x1))
   2: f(s(x1)) -> h(s(x1),s(x1))
   3: g(x1) -> s(x1)

--- S
   1: f(g(x1)) -> h(g(x1),g(x1))
   2: f(s(x1)) -> h(s(x1),s(x1))
   3: g(x1) -> s(x1)