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:
  a -> c
  a -> d
  s(c) -> t(k)
  f(x) -> s(x)
  s(x) -> x
  t(x) -> x
  f(x) -> x

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