YES

Proof:
This system is confluent.
By \cite{ALS94}, Theorem 4.1.
This system is of type 3 or smaller.
This system is strongly deterministic.
There are no critical pairs.
This system is of type 3 or smaller.
This system is deterministic.
Call external tool:
ttt2 - trs 30
Input:
  F(x) -> F(A)
  F(x) -> x
  e(x) -> x
  e(x) -> x
  F(x) -> x

 Containment Processor: loop length: 1
                        terms:
                         F(x)
                        context: []
                        substitution:
                         x -> A()
  Qed
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 optimized U(R).
Call external tool:
ttt2 - trs 30
Input:
  ?1(B, x) -> F(A)
  F(x) -> ?1(x, x)
  e(x) -> x

 LPO Processor:
  precedence:
   B > F > e ~ A ~ ?1
  problem:
   
  Qed