On closure of configurations in freely generated projective planes

Let $\mathcal{F}$ be an arbitrary freely generated projective plane. Based on Shirshov's combinatorial method, we introduce the notion of a reduced configuration in $\mathcal{F}$. We prove that for every subplane $\mathcal{P}$ generated in $\mathcal{F}$ by some configuration $\mathcal{B}$, there is a reduced configuration $\mathcal{B}'$ such that $\mathcal{P}$ is freely generated by $\mathcal{B}'$.