Theorem CS-10. Support (10) for the CS conjecture.

\{ \begin{matrix}(xy)z = x(yz) \\ x_{1}x_{2} ⋯ x_{n} = x_{2} ⋯ x_{n}x_{1} \end{matrix} \} ⇒ \{ \begin{matrix}∀m ≥ ⌈n/2⌉, x^{m}y^{m} = y^{m}x^{m} \\ ∀m ≥ n − 1, (xy)^{m} = x^{m}y^{m} \end{matrix} \} .