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:
  ?2(x, x) -> x
  ?1(a, x) -> ?2(b, x)
  f(x) -> ?1(x, x)
  a -> b

 DP Processor:
  DPs:
   ?1#(a(),x) -> ?2#(b(),x)
   f#(x) -> ?1#(x,x)
  TRS:
   ?2(x,x) -> x
   ?1(a(),x) -> ?2(b(),x)
   f(x) -> ?1(x,x)
   a() -> b()
  TDG Processor:
   DPs:
    ?1#(a(),x) -> ?2#(b(),x)
    f#(x) -> ?1#(x,x)
   TRS:
    ?2(x,x) -> x
    ?1(a(),x) -> ?2(b(),x)
    f(x) -> ?1(x,x)
    a() -> b()
   graph:
    f#(x) -> ?1#(x,x) -> ?1#(a(),x) -> ?2#(b(),x)
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 1/4