= 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.
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