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

 DP Processor:
  DPs:
   f#(x,y) -> ?1#(x,x,y)
  TRS:
   a() -> t(c())
   a() -> t(d())
   ?1(t(z),x,y) -> z
   f(x,y) -> ?1(x,x,y)
   g(x,x) -> h(x,x)
  TDG Processor:
   DPs:
    f#(x,y) -> ?1#(x,x,y)
   TRS:
    a() -> t(c())
    a() -> t(d())
    ?1(t(z),x,y) -> z
    f(x,y) -> ?1(x,x,y)
    g(x,x) -> h(x,x)
   graph:
    
   Qed