Folding condition

For involutory generators, the folding condition requires that simple multiplication never preserve length and that simultaneous left and right ascents either combine to a two-step ascent or fold: if both $s_{i}w$ and $w{s}_j$ have length $\ell (w)+1$, then either $\ell (s_{i}w{s}_j)=\ell (w)+2$ or $w=s_{i}w{s}_j$.

For generators $s_i,s_j$ with $m_{ij}<\infty$, the braid relation equates the two alternating words of length $m_{ij}$ beginning with $s_i$ and $s_j$, respectively. When $m_{ij}=2$, it says that the generators commute.