Let $F_n$ be a free group of rank n and consider all possible non-degenerate length functions on $F_n$. 

Could I be directed to a reference that give two non-trivial non-power-conjugate elements $g,h \in F_n$ (i.e. no power of $g$ is conjugate to a power of $h$) such that there is some $K>1$ so that for any length function we have: 
$$
\|g\|_T \geq K \cdot \|h\|_T,
$$
where $\|\cdot\|_T$ denote translation length for some $T \in \operatorname{CV}_n$? Obviously, we have this if $h^K=g$, but I specifically want a pair of elements that are not powers of one another.