User blog comment:KamafaDelgato021469/My extension to chained arrow notation/@comment-25601061-20180627171419/@comment-5529393-20180627193210

Nah, it's less than ω2 + 1.

a→→b is a regular chain of length b.

a→→b→→c→→d... is a regular chain of length b*c*d..., so a→→→b = a→→a→→a→→...→→a is a regular chain of length ab-1

a→→→→b = a→→→a→→→a...→→→a with length b = a→→a→→a...→→a with length ab-1 = a→a→a→...→a with length aa b-1-1.

Each additional arrow will result in a regular Conway chain length an exponential tower one higher, so

a →n a is roughly fω^2(a^^(n-1)).