YES

Proof:
This system is confluent.
By \cite{ALS94}, Theorem 4.1.
This system is of type 3 or smaller.
This system is strongly deterministic.
There are no critical pairs.
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:
  f(x) -> a
  f(x) -> x
  f(x) -> x

 DP Processor:
  DPs:
   
  TRS:
   f(x) -> a()
   f(x) -> x
  Qed