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

 DP Processor:
  DPs:
   s#(a()) -> c#()
   s#(b()) -> c#()
   c#() -> t#(k())
   c#() -> t#(l())
   f#(x) -> s#(x)
   g#(x,x) -> h#(x,x)
  TRS:
   s(a()) -> c()
   s(b()) -> c()
   c() -> t(k())
   c() -> t(l())
   f(x) -> s(x)
   g(x,x) -> h(x,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) -> x
  TDG Processor:
   DPs:
    s#(a()) -> c#()
    s#(b()) -> c#()
    c#() -> t#(k())
    c#() -> t#(l())
    f#(x) -> s#(x)
    g#(x,x) -> h#(x,x)
   TRS:
    s(a()) -> c()
    s(b()) -> c()
    c() -> t(k())
    c() -> t(l())
    f(x) -> s(x)
    g(x,x) -> h(x,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) -> x
   graph:
    f#(x) -> s#(x) -> s#(b()) -> c#()
    f#(x) -> s#(x) -> s#(a()) -> c#()
    s#(b()) -> c#() -> c#() -> t#(l())
    s#(b()) -> c#() -> c#() -> t#(k())
    s#(a()) -> c#() -> c#() -> t#(l())
    s#(a()) -> c#() -> c#() -> t#(k())
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 6/36