On free subgroup in Artin group with tree-structure

Let $G$ be finitely generated Artin group with tree-structure defined by the presentation $G = <a_1, ..., a_n; <a_ia_j>^{m_{ij}}=<a_ j a_ i>^{m_{ji}}, i ,j = \overline{1, n}>$, where $m_{ij}$ is number that corresponds to symmetrical matrix of Coxeter, and $m_{ij}\geq 2, i \ne j$ a group $G$ matches the end coherent tree-graph $\Gamma$ such that if the tops of some edge $e$ of the graph $\Gamma$ match the form $a_i$ and $a_j$, then the edge $e$ corresponds to the ratio of the species $<a_ia_j>^{m_{ij}}=<a_ j a_ i>^{m_{ji}}$.
Artin groups with a tree-structure was introduced by V. N. Bezverkhnii, theirs algorithmic problems were considered by V. N. Bezverkhnii and O. Y. Platonova (Karpova).
The group $G$ can be represented as the tree product 2-generated of the groups, united by a cyclic subgroups. We proceed from the graph $\Gamma$ of the group $G$ to the graph $\overline{\Gamma}$ the following follows: the tops of some edge $\overline{e}$ of the graph $\overline{\Gamma}$ put in correspondence Artin groups the two forming $G_{ij} = <a_i, a_j; <a_ia_j>^{m_{ij}}=<a_ j a_ i>^{m_{ji}}>$ and $G_{jk} = <a_j, a_k; <a_ja_k>^{m_{jk}}=<a_ k a_ j>^{m_{kj}} >$, and edge $\overline{e}$ will match cyclic subgroup $<a_j>$.
This paper considers the theorem on the freedom of the Artin groups with a tree-structure: let $H$ be finitely generated subgroup of an Artin group $G$ with a tree-structure, while for any $g \in G$ and every subgroup $G_{ij}$, $i\neq j$, executed equality $gHg^{-1}\cap G_{ij} =E$ then $H$ is free.
In the proof of use of the ideas V. N. Bezverkhnii on bringing many forming of the subgroup to a special set.