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:
  s(a) -> c
  s(b) -> c
  c -> t(k)
  c -> t(l)
  ?1(z, x) -> z
  f(x) -> ?1(s(x), x)
  g(x, x) -> h(x, x)

 DP Processor:
  DPs:
   s#(a()) -> c#()
   s#(b()) -> c#()
   f#(x) -> s#(x)
   f#(x) -> ?1#(s(x),x)
  TRS:
   s(a()) -> c()
   s(b()) -> c()
   c() -> t(k())
   c() -> t(l())
   ?1(z,x) -> z
   f(x) -> ?1(s(x),x)
   g(x,x) -> h(x,x)
  TDG Processor:
   DPs:
    s#(a()) -> c#()
    s#(b()) -> c#()
    f#(x) -> s#(x)
    f#(x) -> ?1#(s(x),x)
   TRS:
    s(a()) -> c()
    s(b()) -> c()
    c() -> t(k())
    c() -> t(l())
    ?1(z,x) -> z
    f(x) -> ?1(s(x),x)
    g(x,x) -> h(x,x)
   graph:
    f#(x) -> s#(x) -> s#(b()) -> c#()
    f#(x) -> s#(x) -> s#(a()) -> c#()
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 2/16