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) -> g(x, h(a, x), h(a, h(a, x)))
  f(x) -> h(a, h(a, x))
  f(x) -> h(a, x)
  h(a, a) -> i(b)
  h(a, b) -> i(c)
  h(b, b) -> i(d)
  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
  i(x) -> x

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