YES

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

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

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