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
  b -> c
  ?1(x, x) -> x
  f(x) -> ?1(a, x)

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