The rat-group knot-group conjecture

A rat-group is obtained by deleting the final relator from an Artin $n$-presentation of the trivial group, so it has a deficiency-one presentation. A knot group is characterized by an Artin presentation satisfying

$$\prod_{i=1}^n s_i y_i s_i^{-1}=\prod_{i=1}^n y_i$$

in the free group $F(y_1,\ldots,y_n)$. The rat-group conjecture. Every rat-group is a knot group; equivalently, a rat-group has a presentation satisfying the displayed Artin relation. The statement appears after the paper's discussion of rat-groups and is presented as a characterization, but the supplied text gives no separate resolution status. It is therefore recorded as open pending verification against the cited results.