User blog comment:Mh314159/new YIP notation/@comment-39585023-20190708030201/@comment-35470197-20190708030422

We have \begin{eqnarray*} f_a(b) & \sim & F_{2a}(b) \\ \{m\}_y(x) & \sim & F_{2 \omega \times (1+m) + 2y}(x) \\ [a] & \sim & F_{2 \omega \times (2+\omega) + 1}(a), \end{eqnarray*} and this is the limit of the current notation. The rest system does not terminate because it includes diverging loops. For example, in order to compute \([a,1]\), you need to compute \([x,1]\) for an \(x\) greater than \(a\).

As I recommended in the comment below, it is good to specify the dependence for variables in order to avoid such a mistake, For example, if you write \(\{m\}_y(x)_{a,b}\) instead of \(\{m\}_y(x)\), it is easier to find the error of the illegal call of \([x,b]\) in the definition of \([a,b]\).