  Ackermann's function can be expressed using an iterative algorithm, which
essentially takes the form of a term rewriting system. Although the termination
of this algorithm is far from obvious, its equivalence to the traditional
recursive formulation--and therefore its totality--has a simple proof in
Isabelle/HOL. This is a small example of formalising mathematics using a proof
assistant, with a focus on the treatment of difficult recursions.
