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

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