Fig. 2.

Illustration of the substring selector ${\mathit{\varphi }}_{n-1}(·)$ with three examples. In the contraction operation, a substring inside of the outermost closed parentheses (green) is reduced to the character in its first position (red). The extraction operation is to remove the rest (black) of the last $n-1$ ($=9$) characters from the reduced string. The corresponding graphs are shown on the right where the atoms in the boxes indicate the last characters in the inputs of ${\mathit{\varphi }}_{n-1}(·)$ (left)