Tarjan's proof of inverse* Ackermann bound is hard to understand; it's much easier to understand the proof of the log*(n) bound, which is also an extremely slow growing function: https://people.eecs.berkeley.edu/~vazirani/algorithms/chap5....

where log* is the iterated log function; i.e. the number of times you have to apply log repeatedly until you reach a value of 1 or smaller. For reference, log_2*(10^10000) = 5.

https://en.wikipedia.org/wiki/Iterated_logarithm