User blog comment:Wythagoras/Dollar function: final version/@comment-5529393-20131116082407

Concerning Extended Bracket Notation, it doesn't appear to mirror the Buchholz hydra. The Buchholz hydra finds the first ancestor with label less than the current label, and replicates the entire subtree starting from that first ancestor, with the current label replaced by 0. I don't see that process anywhere in your rules.

What is a$[0]_c when c > 1? It doesn't seem to be addressed by your rules.