 is a \(\beta\)-reduction sequence from \((\lambda x[x])a\) to \(a\). If \(a\) is a variable, then this \(\beta\)-reduction sequence cannot be prolonged, and there are no other \(\beta\)-reduction sequences commencing with \((\lambda x[x])a\); thus, the set of \(\beta\)-reduction sequences commencing with \((\lambda x[x])a\) is finite and contains no infinite sequences.