Consider ins-del systems of size (1, 0, 0; 1, 0, 0) extended with one-sided substitution rules; the increase in computational power is quite significant: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \text {INS}_1^{0,0} \text {DEL}_1^{0,0}\subset \text {INS}_1^{1,0} \text {DEL}_1^{1,0}\subset \text {INS}^{1,0}_1 \text {DEL}^{1,0}_1\text {SUB}^{1,0} =\text {INS}^{0,0}_1 \text {DEL}^{0,0}_1\text {SUB}^{1,0} \end{aligned}$$\end{document} Both inclusions are proper.
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