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