Let $G$ be a group. A length function on $G$ is a function $L\colon G \to \Rset^+$ satisfying: \begin{eqnarray*} L(e) & = & 0, \\ L(g) & = & L(g^{-1}), \quad\forall g \in G, \\ L(g_1 g_2) & \leq & L(g_1) + L(g_2), \quad\forall g_1, g_2 \in G. \end{eqnarray*}