User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 2/@comment-7484840-20130530171941/@comment-7484840-20130601125749

n![1, [m_1, ..., m_n]] w/[1] = n!1, [1, ..., m_nw/[1], [m_1-1, ..., m_n]] w/[1] = n!1, [1, ..., m_nw/[1], [m_1-1, ..., m_n]] w/[1]... this process of making new brackets in the 1st slot will be repeated a lot before there is a non-1 main entry. I am fairly sure the rule does eventually terminate, because the numbers in the brackets are slowly dropping, and it does not increase the length of any brackets without using a w/ operator.

It is worth remembering that [m_1, ..., m_n] would really be [[...[[n],...],.........],...m_n]