Thickness of Feathers

Briefly, a feather is a semigroup derivation diagram with the labels on the edges removed. In this paper, we are concerned with possible definitions for the thickness of a feather.

A major open problem is whether the word problem is solvable for semigroup presentations with one defining relation. It is known that word problems for semigroup presentations are solvable if the number of regions in minimal derivation diagrams is bounded. For some definitions for thickness, the number of regions in a derivation diagram over a presentation with one relation will be bounded if the thickness of the diagram is bounded.