Characterization of bi-UFS positive semirings

Let $S$ be a positive semiring. Bi-UFS characterization conjecture. The semiring $S$ is a bi-UFS if and only if

$$S=\mathbb{N}_0.$$

The paper notes that $\mathbb{N}_0$ is a bi-UFS and presents no other examples; the conjecture asserts that these are the only positive semirings with this property.