YES

   1: f(a()) -> f(g(b(),b()))
   2: a() -> g(c(),c())
   3: c() -> d()
   4: d() -> b()
   5: b() -> d()

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

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