User blog comment:Deedlit11/Bignum Bakeoff appetizer/@comment-31663462-20171109233955


 * Ruby, 103 bytes**

f=->a,n{c,d,e=a;a==0?n:a==c ?a-1:e==1||d==0?c:c,d,f[e,n,d-1,c]};h=0,k=9,0;(h=f[h,k*=k])while h!=1;k

Try it online:

https://tio.run/##FcpLCsIwGEXhrdSZlRtIhiZcu5CQQZoHv0QyEESKde3Rjg58nOdr3caoVLeI/knIKIwuknrp9p80LVEZW0iz7/ngZL0/vuoLegjIyiCFrxNqNF6h3VlYvaBd2ML8lvujTHKicW2MHw