There cannot be any overlap between register arcs where the corresponding tokens were not in the registers simultaneously: the Clear transition updates the book-keeping constant last to be the rightmost vertex associated with  the registers being cleared, and subsequent actions cannot introduce crossed arcs to the last token or to its left (by the β 1 > last and σ 1 > last preconditions on storing and register-stack arcs, respectively).
each set of tokens that were in registers simultaneously defines a crossing interval.