The equivalence of maximal matching and maximal independent matching

Let $athsf{MM}$ denote the maximal matching principle and let $athsf{MIM}$ denote the maximal independent matching principle, both formulated over $peratorname{\mathsf{RCA}}_0$. Let $athsf{PM}$ denote the perfect matching principle.

The computational-strength conjecture. $athsf{MM}$ and $athsf{MIM}$ are equivalent over $peratorname{\mathsf{RCA}}_0$, i^1_1\text{-}\mathsf{TR}}_0 proves $athsf{PM}$, and i^1_2\text{-}\mathsf{CA}}_0 proves $athsf{MM}$.

These assertions compare the reverse-mathematical strength of matching principles. The source presents them as a conjectural computational-strength statement; the supplied status is unknown.