User blog comment:Googleaarex/Make an extension of the notation/@comment-25371339-20140923221002/@comment-25371339-20140924181309

Let define ^ = ^1, * = ^2, and ' = ^3.

The limit of this extension is a-^a-^ a-^ ...^ a-^ a-^ a-b-b -b ... -b -b -b, or something like that.