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:
  ?1(B, x) -> F(A)
  F(x) -> ?1(x, x)
  or(x, y) -> x
  or(x, y) -> y

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