Bi-torsion-free threshold for an additive endomorphism of a non-associative ring

Definition
Suppose $$R$$ is a non-associative ring and $$f:R \to R$$ is an endomorphism of the additive group of $$R$$. The bi-torsion-free threshold for $$f$$ is the largest positive integer $$m$$ such that, for all $$n \le m$$, and all $$i,j$$ such that $$i + j = n$$, the defining ingredient::torsion-free threshold for the subring of $$R$$ generated by $$f^i(R) * f^j(R)$$ is at least equal to $$n$$.