A GROUP-EMBEDDABLE NON-AUTOMATIC SEMIGROUP WHOSE UNIVERSAL GROUP IS AUTOMATIC
Alan J. Cain · Glasgow Mathematical Journal · 2006
Answering a question of Hoffmann and of Kambites, an example is exhibited of a finitely generated semigroup $S$ such that $S$ embeds in a group and $S$ is not automatic, but the universal group of $S$ is automatic.