An element $f\in\mathcal{T}_{n}$ with $\vvvert f\vvvert_{\mathcal{T}_{n}}=1$ is said to be regular in $z_{n}$ of degree $d$ if its reduction $\bar{f}=\lambda(z_{n})^{d}+\sum_{0\leq i\leq d-1}c_{i}(z_{n})^{d-i}$ in $\bar{\mathcal{T}_{n}}$ where $\lambda\in k^{\times}$ and $c_{i}\in\bar{k}[z_{1},\dots,z_{n-1}]$.