  Over the recent years, the theory of rewriting has been used and extended in
order to provide systematic techniques to show coherence results for strict
higher categories. Here, we investigate a further generalization to Gray
categories, which are known to be equivalent to tricategories. This requires us
to develop the theory of rewriting in the setting of precategories, which
include Gray categories as particular cases, and are adapted to mechanized
computations. We show that a finite rewriting system in precategories admits a
finite number of critical pairs, which can be efficiently computed. We also
extend Squier's theorem to our context, showing that a convergent rewriting
system is coherent, which means that any two parallel 3-cells are necessarily
equal. This allows us to prove coherence results for several well-known
structures in the context of Gray categories: monoids, adjunctions, Frobenius
monoids.
