YES

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

@Development Closedness
--- R
   1: f(a(),a()) -> g(f(a(),a()))
   2: a() -> b()
   3: f(b(),x) -> g(f(x,x))
   4: f(x,b()) -> g(f(x,x))

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