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(y, x) -> g(y)
  f(x) -> ?1(x, x)

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