AEJ-E asphericity conjecture for positive relative presentations

Let $l>0$ and $k>0$ with $l\neq k$, and let $\mathcal{Q}$ be the relative presentation considered in the paper. Define condition (AEJ-E) by the following alternatives: (i) $g=h^2$, $6<|h|<\infty$, $l<k<2l$; (ii) $h=g^2$, $6<|g|<\infty$, $k<l<2k$; (iii) $h=g^2$, $6<|g|<\infty$, $l<k<2l$; or (iv) $g=h^2$, $6<|h|<\infty$, $k<l<2k$. AEJ-E asphericity conjecture. If (AEJ-E) holds, then $\mathcal{Q}$ is diagrammatically reducible and hence aspherical. The preceding theorem establishes this conclusion when (AEJ-E) does not hold, while the authors state that they do not expect non-aspherical presentations in the exceptional case; the supplied text gives no proof or disproof of the conjecture.