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:
  f(x) -> x
  g(d, x, x) -> A
  h(x, x) -> g(x, x, f(k))
  c -> e'
  a -> c
  a -> d
  b -> c
  b -> d
  c -> e
  c -> l
  k -> l
  k -> m
  d -> m
  h(x, y) -> x
  h(x, y) -> y
  g(x, y, z) -> x
  g(x, y, z) -> y
  g(x, y, z) -> z
  f(x) -> x

 DP Processor:
  DPs:
   h#(x,x) -> k#()
   h#(x,x) -> f#(k())
   h#(x,x) -> g#(x,x,f(k()))
   a#() -> c#()
   a#() -> d#()
   b#() -> c#()
   b#() -> d#()
  TRS:
   f(x) -> x
   g(d(),x,x) -> A()
   h(x,x) -> g(x,x,f(k()))
   c() -> e'()
   a() -> c()
   a() -> d()
   b() -> c()
   b() -> d()
   c() -> e()
   c() -> l()
   k() -> l()
   k() -> m()
   d() -> m()
   h(x,y) -> x
   h(x,y) -> y
   g(x,y,z) -> x
   g(x,y,z) -> y
   g(x,y,z) -> z
  TDG Processor:
   DPs:
    h#(x,x) -> k#()
    h#(x,x) -> f#(k())
    h#(x,x) -> g#(x,x,f(k()))
    a#() -> c#()
    a#() -> d#()
    b#() -> c#()
    b#() -> d#()
   TRS:
    f(x) -> x
    g(d(),x,x) -> A()
    h(x,x) -> g(x,x,f(k()))
    c() -> e'()
    a() -> c()
    a() -> d()
    b() -> c()
    b() -> d()
    c() -> e()
    c() -> l()
    k() -> l()
    k() -> m()
    d() -> m()
    h(x,y) -> x
    h(x,y) -> y
    g(x,y,z) -> x
    g(x,y,z) -> y
    g(x,y,z) -> z
   graph:
    
   Qed