 Finite-state row shortening of a combing diagram

For a null loop of length $n$, a horizontal row of its combing diagram is encoded by an ordered $n$-tuple of rung words of length at most $K$. If there are $D$ such words, there are at most $D^n$ row types. Between two identical labelled rows one can delete the entire intervening annular band and glue the equal boundary paths. Repeating this leaves at most $D^n$ layers of $n$ bounded-perimeter cells. Thus a synchronous combable group has a recursive exponential isoperimetric bound. This does not require the combing language to be regular or computable.