User blog comment:Boboris02/Quickly-extending linear hydra/@comment-25337554-20161129231813

I think your hydra is as strong as up-arrow notation.

First, 0 is just an increment.

The leftmost 1 becomes several 0's, so 1 is as strong as doubling.

The leftmost 2 becomes several 1's, so 2 is as strong as exponention.

Inductively, your entire hydra system goes as strong as f_{\omega}(n).

(Note: You add a:{b}=a^b to the last step of the hydra, but it is useless if a and b is bigger than tetrational numbers)