YES

1 decompositions
 #1 -----------
   1: f(x1) -> g(f(x1))
   2: h(x2) -> p(h(x2))
   3: f(x3) -> h(f(x3))
   4: g(x4) -> p(p(h(x4)))

@Rule Labeling
--- R
   1: f(x1) -> g(f(x1))
   2: h(x2) -> p(h(x2))
   3: f(x3) -> h(f(x3))
   4: g(x4) -> p(p(h(x4)))

--- S
   1: f(x1) -> g(f(x1))
   2: h(x2) -> p(h(x2))
   3: f(x3) -> h(f(x3))
   4: g(x4) -> p(p(h(x4)))