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
  b -> c
  f(x) -> x
  f(x) -> a
  f(x) -> x

 DP Processor:
  DPs:
   f#(x) -> a#()
  TRS:
   a() -> c()
   b() -> c()
   f(x) -> x
   f(x) -> a()
  TDG Processor:
   DPs:
    f#(x) -> a#()
   TRS:
    a() -> c()
    b() -> c()
    f(x) -> x
    f(x) -> a()
   graph:
    
   Qed