Guba–Sapir closure conjecture for diagram groups

Let $\mathcal{K}$ be a directed $2$-complex, let $u$ be a $1$-path, and let $H$ be a subgroup of the diagram group $\mathrm{DG}(\mathcal{K},u)$. A subgroup is closed for components if, whenever it contains a diagram, it contains all components of that diagram. The closure $\mathrm{Cl}(H)$ is the subgroup generated by all diagrams accepted by the closure construction from $H$. Guba–Sapir's conjecture. The closure $\mathrm{Cl}(H)$ is the minimal subgroup of $\mathrm{DG}(\mathcal{K},u)$ which contains $H$ and is closed for components. The conjecture is known in some special cases, but remains open for general diagram groups.