Algorithmic conjecture for detecting zero-divisor ACR

Let $(G,\kappa^*)$ be a mass-action system with $n$ species and rational-number rate constants, and let $I$ be its steady-state ideal. For each species $X_i$, Algorithm~ computes a reduced Gröbner basis of $I$ using an elimination order for all variables except $x_i$, and outputs pairs $(X_i,\alpha)$ from positive roots of the resulting univariate basis element or of leading coefficients. Zero-divisor ACR detection conjecture. If $(G,\kappa^*)$ has zero-divisor ACR in species $X_i$ with ACR-value $\alpha$, then $(X_i,\alpha)$ is one of the outputs of the algorithm. This would provide an algebraic procedure for finding ACR species and values even when the relevant factor is a zero-divisor modulo the steady-state ideal; the source does not state a resolution of the conjecture.