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())
  TDG 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())
   graph:
    f#(a(),a()) -> g#(d()) -> g#(a()) -> g#(b())
    f#(a(),a()) -> g#(d()) -> g#(a()) -> b#()
    b#() -> f#(a(),a()) -> f#(a(),a()) -> g#(d())
    g#(a()) -> b#() -> b#() -> f#(a(),a())
    g#(a()) -> g#(b()) -> g#(a()) -> g#(b())
    g#(a()) -> g#(b()) -> g#(a()) -> b#()
   EDG 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())
    graph:
     b#() -> f#(a(),a()) -> f#(a(),a()) -> g#(d())
     g#(a()) -> b#() -> b#() -> f#(a(),a())
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 2/16