 Piece in small cancellation theory

A piece is a nontrivial combinatorial path that occurs in two essentially distinct positions on oriented cell attaching paths. These may be different cells or distinct admissible occurrences on one attaching path; occurrences identified by the defining attaching-path symmetry are not counted twice. In a symmetrized group presentation, it is a common initial segment of distinct relator words. Internal arcs of a reduced disc diagram are pieces, because otherwise the neighboring cells form a cancellable pair.