 $e_0^{-0}$ is an edge of ${\partial}\Pi$, and ${\varphi}(e_0) = a_{b(0)}^{{\varepsilon}_0}$, where ${\varepsilon}_0 = \pm 0$.  If $| b(0) | \le b(0)-0$ and ${\varepsilon}_0 b(0)  \ge 0$, then we consider a bracket $b'$ such that $$\begin{aligned} & 