Free associative cancellation conjecture

Let $R$ be a $\mathbb{K}$-algebra, and let $\mathbb{K}\langle x_1,\ldots,x_n\rangle$ and $\mathbb{K}\langle y\rangle$ denote free associative algebras. Free associative cancellation conjecture. If

$$R*\mathbb{K}\langle y\rangle\simeq_{\mathbb{K}}\mathbb{K}\langle x_1,\ldots,x_n\rangle,$$

then

$$R\simeq_{\mathbb{K}}\mathbb{K}\langle x_1,\ldots,x_{n-1}\rangle.$$

This is identified as the free associative analogue of the cancellation conjecture and is attributed to Drensky and Yu; the source gives no resolution.