 for the word $W$.  Let $B$ be a finite set of [pseudobracket]{}s for $W$, perhaps, $B$ is empty. We say that $B$ is a [*pseudobracket system*]{} if, for every pair $b, c \in B$ of distinct [pseudobracket]{}s, either $b(0) \le c(0)$ or $c(0) \le b(0)$. 