 Definition For \(\lambda\)-terms \(A\) and \(B\), we say that \(A =_{\beta} B\) if either \(A \equiv B\) or there exists a sequence \(s_1 , \ldots s_n\) starting with \(A\), ending with \(B\), and whose adjacent terms \((s_k,s_{k+1})\) are such that either \(s_k \rhd_{\beta ,1} s_{k+1}\) or \(s_{k+1} \rhd_{\beta ,1} s_k\).