YES

   3: a() -> d()
   5: f(c()) -> b()
   6: d() -> c()

@Jouannaud and Kirchner's criterion
--- R
   3: a() -> d()
   5: f(c()) -> b()
   6: d() -> c()

--- S
   3: a() -> d()
   5: f(c()) -> b()
   6: d() -> c()


NOTE: input TRS is reduced

original is
   1: f(a()) -> b()
   2: f(a()) -> f(c())
   3: a() -> d()
   4: f(d()) -> b()
   5: f(c()) -> b()
   6: d() -> c()

reduced to
   3: a() -> d()
   5: f(c()) -> b()
   6: d() -> c()