YES

Proof:
This system is quasi-decreasing.
By \cite{O02}, p. 214, Proposition 7.2.50.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to U(R).
Call external tool:
ttt2 - trs 30
Input:
  a -> c
  g(a) -> h(b)
  h(b) -> g(c)
  ?1(h(z), x) -> z
  f(x) -> ?1(g(x), x)

 LPO Processor:
  precedence:
   f > a > b > ?1 ~ h ~ g ~ c
  problem:
   
  Qed