Definition:Reduction of Group Word on Set

Definition
Let $X$ be a set.

Let $w$ be a group word on $X$.

A reduction of $w$ is a finite sequence of group words $(w^{(0)}, \ldots, w^{(n)})$ such that:
 * $w^{(0)} = w$
 * $w_{i+1}$ is an elementary reduction of $w_i$, for all $i \in \{0, \ldots, n-1\}$
 * $w^{(n)}$ is reduced

Also see

 * Definition:Reduced Form of Group Word