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

 DP Processor:
  DPs:
   s#(k()) -> a#()
   s#(k()) -> t#(a())
   s#(l()) -> a#()
   s#(l()) -> t#(a())
   g#(x,x) -> h#(x,x)
   f#(x,y) -> s#(x)
  TRS:
   a() -> c()
   a() -> d()
   b() -> c()
   b() -> d()
   s(k()) -> t(a())
   s(l()) -> t(a())
   g(x,x) -> h(x,x)
   f(x,y) -> y
   f(x,y) -> s(x)
   h(x,y) -> x
   h(x,y) -> y
   s(x) -> x
   g(x,y) -> x
   g(x,y) -> y
   t(x) -> x
   f(x,y) -> x
  TDG Processor:
   DPs:
    s#(k()) -> a#()
    s#(k()) -> t#(a())
    s#(l()) -> a#()
    s#(l()) -> t#(a())
    g#(x,x) -> h#(x,x)
    f#(x,y) -> s#(x)
   TRS:
    a() -> c()
    a() -> d()
    b() -> c()
    b() -> d()
    s(k()) -> t(a())
    s(l()) -> t(a())
    g(x,x) -> h(x,x)
    f(x,y) -> y
    f(x,y) -> s(x)
    h(x,y) -> x
    h(x,y) -> y
    s(x) -> x
    g(x,y) -> x
    g(x,y) -> y
    t(x) -> x
    f(x,y) -> x
   graph:
    f#(x,y) -> s#(x) -> s#(l()) -> t#(a())
    f#(x,y) -> s#(x) -> s#(l()) -> a#()
    f#(x,y) -> s#(x) -> s#(k()) -> t#(a())
    f#(x,y) -> s#(x) -> s#(k()) -> a#()
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 4/36