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
  c -> e
  c -> k
  d -> k
  f(x) -> x
  g(x, x) -> C
  g(x, x) -> A
  h(x) -> i(x, x)
  h(x) -> x
  g(x, y) -> x
  g(x, y) -> y
  f(x) -> x
  i(x, y) -> x
  i(x, y) -> y

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