We explain how recent developments in game semantics can be applied to reasoning about equivalence of terms in a non-trivial fragment of Idealized AupLGOL (IA) by expressing sets of complete plays as regular languages. Being derived directly from the fully abstract game semantics for IA, our method of reasoning inherits its desirable theoretical properties. The method is mathematically elementary and formal, which makes it uniquely suitable for automation. We show that reasoning can be carried out using only a meta-language of extended regular expressions, a language for which equivalence is formally decidable.