Consider the procedure PROCX in figure 1.7. It assumes there are other procedures elsewhere that will do some arithmetic (subtraction, multiplication, and less-than comparisons). It also assumes that one can concatenate strings of digits: x ˆy means the string consisting of the digits in x followed by those in y. It works by repeatedly setting new values to u, v, bot, top, and side as the digits of the input are worked through in pairs from left to right.

Figure out what the procedure PROCX is doing. Hint: Trace its behavior when the input is 137641.