 The failure of the diamond property is obvious once we note that \(\textsf{SKKK}\triangleright_1\textsf{KK}(\textsf{KK})\) (only), but \(\textsf{K}(\textsf{KKS})(\textsf{K}(\textsf{KKS}))\) does not reduce in one step to \(\textsf{KK}(\textsf{KK})\).