Definition:Reduced Form of Group Word

Definition
Let $X$ be a set.

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

The reduced form $\operatorname{red}(w)$ of $w$ is the unique reduced word for which there exists a reduction:
 * $w = w^{(0)} \longrightarrow w^{(1)} \longrightarrow \ldots \longrightarrow w^{(n)} = \operatorname{red}(w)$

Also see

 * Definition:Existence and Uniqueness of Reduced Form of Group Word