YES

Proof:
This system is quasi-decreasing.
By \cite{A14}, Theorem 11.5.9.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to V(R) + Emb.
Call external tool:
ttt2 - trs 30
Input:
  f(x) -> x
  f(x) -> s(x)
  s(a) -> t(b)
  a -> b
  s(x) -> x
  t(x) -> x
  f(x) -> x

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