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:
  ?1(b, x) -> a
  f(x, x) -> ?1(g(x), x)

 DP Processor:
  DPs:
   f#(x,x) -> ?1#(g(x),x)
  TRS:
   ?1(b(),x) -> a()
   f(x,x) -> ?1(g(x),x)
  TDG Processor:
   DPs:
    f#(x,x) -> ?1#(g(x),x)
   TRS:
    ?1(b(),x) -> a()
    f(x,x) -> ?1(g(x),x)
   graph:
    
   Qed