Let $S_n$ be the symmetric group generated by simple reflections $s_1, \ldots, s_{n-1}$.
Given a word $s_{i_1} \cdots s_{i_m}$ in $S_n$, is there some method to check that $s_{i_1} \cdots s_{i_m}$ is reduced?
For example, in $S_8$, is the word $s_6 s_2 s_4 s_3 s_2 s_1 s_5 s_4 s_3 s_2 s_6 s_5 s_4 s_3 s_7 s_6 s_5 s_4$ reduced?
Thank you very much.