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) -> e
  f(x) -> d
  h(x, x) -> A
  h(x, y) -> x
  h(x, y) -> y
  f(x) -> x

 DP Processor:
  DPs:
   
  TRS:
   f(x) -> e()
   f(x) -> d()
   h(x,x) -> A()
   h(x,y) -> x
   h(x,y) -> y
   f(x) -> x
  Qed