 For any set \(S\) we denote by \(S^*\) the set of all finite sequences of elements of \(S\), including the empty sequence \((\ )\). If \(\alpha = (a_1 ,\ldots ,a_n)\) is in \(S^*\), then \(n\) is called the length of \(\alpha\) and is denoted by \(\abs{\alpha}\). If \(m \in \bN\), and \(\alpha\) is a finite or infinite sequence in \(S\) of length at least \(m\), then we denote by \(\bar{\alpha}(m)\) the finite sequence consisting of the first \(m\) terms of \(\alpha\). Note that \(\bar{\alpha}(0) = (\ )\) and \(\abs{\bar{\alpha}(0)}\) = 0 . If \(\alpha \in S^*\) and \(\beta = \bar{\alpha}(m)\) for some \(m\), we say that \(\alpha\) is an extension of \(\beta\), and that \(\beta\) is a restriction of \(\alpha\).