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(t(x), x) -> x
  f(x) -> ?1(s(x), x)
  s(a) -> t(b)
  a -> b

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