YES

1 decompositions
 #0 -----------
   1: g(a()) -> f(g(a()))
   2: g(b()) -> c()
   3: a() -> b()
   4: f(x) -> h(x,x)
   5: h(x,y) -> c()

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

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