YES

Problem:
 f(a()) -> b()
 f(a()) -> f(c())
 a() -> d()
 f(d()) -> b()
 f(c()) -> b()
 d() -> c()

Proof:
 Uncurry Processor:
  f5(f(),a()) -> b()
  f5(f(),a()) -> f5(f(),c())
  a() -> d()
  f5(f(),d()) -> b()
  f5(f(),c()) -> b()
  d() -> c()
  Ground Confluence Processor:
   confluent by decision procedure.