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

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