Cyclically Dehn-reduced words

Over the symmetrised presentation of Sc toolkit symmetrised relators and pieces, a word $w$ is Dehn-reduced if it is freely reduced and has no literal contiguous segment $s$ that is an initial segment of some $r\in R$ with $\mathrm{\mid }s\mathrm{\mid }>\mathrm{\mid }r\mathrm{\mid }\mathrm{/}2$. Symmetrisation permits the relator segment to start at any corner. A word is cyclically Dehn-reduced if every cyclic rotation of it is Dehn-reduced. Its rotations have the same finite length; the empty word has only itself as a rotation and satisfies both conditions. Equality $\mathrm{\mid }s\mathrm{\mid }=\mathrm{\mid }r\mathrm{\mid }\mathrm{/}2$ is permitted. These conditions concern literal subwords, not equalities in the presented group.

This is Lipschutz §2's “fully reduced” and “cyclically fully reduced” terminology with a local name. No finiteness assumption on $R$ and no effective test is asserted.