YES
TRS:
 {     g(a()) -> g(b()),
          b() -> f(a(), a()),
  f(a(), a()) -> g(d())}
 DP:
  Strict:
   {     g#(a()) -> g#(b()),
         g#(a()) -> b#(),
            b#() -> f#(a(), a()),
    f#(a(), a()) -> g#(d())}
  Weak:
  {     g(a()) -> g(b()),
           b() -> f(a(), a()),
   f(a(), a()) -> g(d())}
  EDG:
   {(b#() -> f#(a(), a()), f#(a(), a()) -> g#(d()))
    (g#(a()) -> b#(), b#() -> f#(a(), a()))}
   SCCS:
    
    Qed