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
  c -> e
  c -> k
  d -> k
  ?1(e, x) -> x
  f(x) -> ?1(x, x)
  ?2(B, x) -> C
  g(x, x) -> ?2(A, x)
  h(x) -> i(x, x)

 DP Processor:
  DPs:
   a#() -> c#()
   a#() -> d#()
   b#() -> c#()
   b#() -> d#()
   f#(x) -> ?1#(x,x)
   g#(x,x) -> ?2#(A(),x)
  TRS:
   a() -> c()
   a() -> d()
   b() -> c()
   b() -> d()
   c() -> e()
   c() -> k()
   d() -> k()
   ?1(e(),x) -> x
   f(x) -> ?1(x,x)
   ?2(B(),x) -> C()
   g(x,x) -> ?2(A(),x)
   h(x) -> i(x,x)
  TDG Processor:
   DPs:
    a#() -> c#()
    a#() -> d#()
    b#() -> c#()
    b#() -> d#()
    f#(x) -> ?1#(x,x)
    g#(x,x) -> ?2#(A(),x)
   TRS:
    a() -> c()
    a() -> d()
    b() -> c()
    b() -> d()
    c() -> e()
    c() -> k()
    d() -> k()
    ?1(e(),x) -> x
    f(x) -> ?1(x,x)
    ?2(B(),x) -> C()
    g(x,x) -> ?2(A(),x)
    h(x) -> i(x,x)
   graph:
    
   Qed