YES

1 decompositions
 #1 -----------
   1: g(a()) -> f(g(a()))
   2: g(b()) -> c(a())
   3: a() -> b()
   4: f(x1) -> h(x1)
   5: h(x1) -> c(b())

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

--- S
   1: g(a()) -> f(g(a()))
   2: g(b()) -> c(a())
   3: a() -> b()
   4: f(x1) -> h(x1)
   5: h(x1) -> c(b())