YES

Problem:
 g(a()) -> g(b())
 b() -> f(a(),a())
 f(a(),a()) -> g(d())

Proof:
 DP Processor:
  DPs:
   g#(a()) -> b#()
   g#(a()) -> g#(b())
   b#() -> f#(a(),a())
   f#(a(),a()) -> g#(d())
  TRS:
   g(a()) -> g(b())
   b() -> f(a(),a())
   f(a(),a()) -> g(d())
  Usable Rule Processor:
   DPs:
    g#(a()) -> b#()
    g#(a()) -> g#(b())
    b#() -> f#(a(),a())
    f#(a(),a()) -> g#(d())
   TRS:
    b() -> f(a(),a())
    f(a(),a()) -> g(d())
   CDG Processor:
    DPs:
     g#(a()) -> b#()
     g#(a()) -> g#(b())
     b#() -> f#(a(),a())
     f#(a(),a()) -> g#(d())
    TRS:
     b() -> f(a(),a())
     f(a(),a()) -> g(d())
    graph:
     b#() -> f#(a(),a()) -> f#(a(),a()) -> g#(d())
     g#(a()) -> b#() -> b#() -> f#(a(),a())
    Restore Modifier:
     DPs:
      g#(a()) -> b#()
      g#(a()) -> g#(b())
      b#() -> f#(a(),a())
      f#(a(),a()) -> g#(d())
     TRS:
      g(a()) -> g(b())
      b() -> f(a(),a())
      f(a(),a()) -> g(d())
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 2/16