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

 LPO Processor:
  precedence:
   f > a > b > h ~ g ~ c
  problem:
   
  Qed