User blog comment:LittlePeng9/Random Turing machines/@comment-5529393-20130408032637

It's interesting that, for high level languages, implementing Goodstein sequences appears to be the most efficient way to code a function of level f_epsilon_0, as you can just manipulate integers  and not more complicated data structures;  but for low level languages, it appears easier to implement Beklemishev worms or Kirby-Paris hydras, as the operations are easier to implement.