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:
  ?2(e', x) -> x
  ?1(e, x) -> ?2(x, x)
  f(x) -> ?1(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

 DP Processor:
  DPs:
   ?1#(e(),x) -> ?2#(x,x)
   f#(x) -> ?1#(x,x)
   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:
   ?2(e'(),x) -> x
   ?1(e(),x) -> ?2(x,x)
   f(x) -> ?1(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()
  TDG Processor:
   DPs:
    ?1#(e(),x) -> ?2#(x,x)
    f#(x) -> ?1#(x,x)
    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:
    ?2(e'(),x) -> x
    ?1(e(),x) -> ?2(x,x)
    f(x) -> ?1(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()
   graph:
    h#(x,x) -> f#(k()) -> f#(x) -> ?1#(x,x)
    f#(x) -> ?1#(x,x) -> ?1#(e(),x) -> ?2#(x,x)
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 2/81