YES

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

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

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