${\displaystyle \begin{array}{cc}\multicolumn{1}{c}{T(x)}& =y\\ \multicolumn{1}{c}{T(y)}& =\mathrm{xy}\end{array}}$

This transformation has the following successive effect (starting with $x$):

${\displaystyle \begin{array}{cc}\multicolumn{1}{c}{x\to T(x)}& =y\\ \multicolumn{1}{c}{y\to T(y)}& =\mathrm{xy}\\ \multicolumn{1}{c}{\mathrm{xy}\to T(x)T(y)}& =\mathrm{yxy}\\ \multicolumn{1}{c}{\mathrm{yxy}\to T(y)T(x)T(y)}& =\mathrm{xyyxy}\\ \multicolumn{1}{c}{\mathrm{xyyxy}\to T(x)T(y)T(y)T(x)T(y)}& =\dots \end{array}}$