How to check whether two elements in a braid group are conjugate using a software?
For example, let $Br_n$ be the braid group generated by $T_1, T_2, \ldots, T_{n-1}$ subject to the relations $ T_i T_j T_i = T_j T_i T_j $ if $|i-j|=1$ and $T_i T_j = T_j T_i$ if $|i-j|>1$.
I want to check that if $T_2 T_1^{-1} T_3^{-1} T_2^{-1} T_5$ and $T_2 T_1 T_3^{-1} T_2^{-1} T_5^{-1}$ are conjugate or not.
Thank you very much.