User blog comment:Chronolegends/improved Egg Notation - Analysis/@comment-28606698-20170427070833

Sorry now I have not time enough to fully become acquainted with your notation , Rules 1-2 seem most recognizable, they correspond for base function of FGH f_0(n) and for case if successor ordinal

Thus, may be, better to write rule 2 as B(R(a+1))R(b)=B^b(R(a))R(b) instead B(R(a+1))R(b)=B^b(R(a)),

Rules 3-5 I still did not analyze, but your notation looks fine. I did not expect it has same limit as and Cascading E-notation. Curiously to see notation which allows to write numbers large than Gongulus even not using arabic numerals.