YES

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

@Development Closedness
--- R
   2: a() -> g(c(),c())
   3: c() -> d()
   4: d() -> b()
   5: b() -> d()

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


NOTE: input TRS is reduced

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

reduced to
   2: a() -> g(c(),c())
   3: c() -> d()
   4: d() -> b()
   5: b() -> d()