Rich words in the block reversal of a word

The block reversal of a word w, denoted by BR(w), is a generalization of the concept of the reversal of a word, obtained by concatenating the blocks of the word in the reverse order. We characterize non-binary and binary words whose block reversal contains only rich words. We prove that for a binary word w, richness of all elements of BR(w) depends on l(w), the length of the run sequence of w. We show that if all elements of BR(w) are rich, then 2≤l(w)≤8. We also provide the structure of such words.