User blog comment:Wythagoras/FGH of Dollar Function new version/@comment-11227630-20131022073239/@comment-1605058-20131022141902

For me, this isn't obvious from your rules that &-> reduces like so. Problem is, you try to make as few rules as possible, so many details we have to figure out ourselves. Simplest example: no rule says when $ disappears. If such "guessing" was allowed, BEAF or FGH would be unboundedly strong with 3 rules, as nothing stops us from defining extreme structures/ordinals.