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:
  h(f(a)) -> c
  h(x) -> j(x)
  c -> j(f(a))
  a -> b
  c -> d
  j(g(b)) -> d
  f(x) -> g(x)
  f(x) -> d
  h(x) -> x
  j(x) -> x
  g(x) -> x
  f(x) -> x

 DP Processor:
  DPs:
   h#(f(a())) -> c#()
   h#(x) -> j#(x)
   c#() -> a#()
   c#() -> f#(a())
   c#() -> j#(f(a()))
   f#(x) -> g#(x)
  TRS:
   h(f(a())) -> c()
   h(x) -> j(x)
   c() -> j(f(a()))
   a() -> b()
   c() -> d()
   j(g(b())) -> d()
   f(x) -> g(x)
   f(x) -> d()
   h(x) -> x
   j(x) -> x
   g(x) -> x
   f(x) -> x
  TDG Processor:
   DPs:
    h#(f(a())) -> c#()
    h#(x) -> j#(x)
    c#() -> a#()
    c#() -> f#(a())
    c#() -> j#(f(a()))
    f#(x) -> g#(x)
   TRS:
    h(f(a())) -> c()
    h(x) -> j(x)
    c() -> j(f(a()))
    a() -> b()
    c() -> d()
    j(g(b())) -> d()
    f(x) -> g(x)
    f(x) -> d()
    h(x) -> x
    j(x) -> x
    g(x) -> x
    f(x) -> x
   graph:
    c#() -> f#(a()) -> f#(x) -> g#(x)
    h#(f(a())) -> c#() -> c#() -> j#(f(a()))
    h#(f(a())) -> c#() -> c#() -> f#(a())
    h#(f(a())) -> c#() -> c#() -> a#()
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 4/36