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(i(z), x, y) -> g(x, y, z)
  ?1(i(y), x) -> ?2(h(a, y), x, y)
  f(x) -> ?1(h(a, x), x)
  h(a, a) -> i(b)
  h(a, b) -> i(c)
  h(b, b) -> i(d)

 DP Processor:
  DPs:
   ?1#(i(y),x) -> h#(a(),y)
   ?1#(i(y),x) -> ?2#(h(a(),y),x,y)
   f#(x) -> h#(a(),x)
   f#(x) -> ?1#(h(a(),x),x)
  TRS:
   ?2(i(z),x,y) -> g(x,y,z)
   ?1(i(y),x) -> ?2(h(a(),y),x,y)
   f(x) -> ?1(h(a(),x),x)
   h(a(),a()) -> i(b())
   h(a(),b()) -> i(c())
   h(b(),b()) -> i(d())
  TDG Processor:
   DPs:
    ?1#(i(y),x) -> h#(a(),y)
    ?1#(i(y),x) -> ?2#(h(a(),y),x,y)
    f#(x) -> h#(a(),x)
    f#(x) -> ?1#(h(a(),x),x)
   TRS:
    ?2(i(z),x,y) -> g(x,y,z)
    ?1(i(y),x) -> ?2(h(a(),y),x,y)
    f(x) -> ?1(h(a(),x),x)
    h(a(),a()) -> i(b())
    h(a(),b()) -> i(c())
    h(b(),b()) -> i(d())
   graph:
    f#(x) -> ?1#(h(a(),x),x) -> ?1#(i(y),x) -> ?2#(h(a(),y),x,y)
    f#(x) -> ?1#(h(a(),x),x) -> ?1#(i(y),x) -> h#(a(),y)
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 2/16