YES

Proof:
This system is quasi-decreasing.
By \cite{A14}, Theorem 11.5.9.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to V(R) + Emb.
Call external tool:
ttt2 - trs 30
Input:
  a -> c
  a -> d
  f(x, y) -> y
  f(x, y) -> c
  f(x, y) -> x
  f(x, y) -> y

 DP Processor:
  DPs:
   
  TRS:
   a() -> c()
   a() -> d()
   f(x,y) -> y
   f(x,y) -> c()
   f(x,y) -> x
  Qed