The inverted five-term generation conjecture for weight-two relations

Let $F$ be a field and let $R_2(F)$ be the weight-two relation subgroup in the modified definition using $F\setminus\{0,1\}$. An inverted five term relation is a relation obtained by applying the involution $[x]\mapsto-[1-x]$ to a five-term relation. The inverted five-term generation conjecture. The group $R_2(F)$ is the subgroup generated by inverted five term relations. If true, this gives the modified weight-two relation group an explicit presentation analogous to the classical five-term presentation.