Problem $\backslash (3(30\backslash$mathrm$\{$Pts$\})\backslash )$ A Minsky machine $[1]$ consists of a finite set of registers, $\backslash ($ r$\_\{1\},$ r$\_\{2\},\backslash$ldots$,$ r$\_\{$k$\}\backslash ),$ each capable of holding an arbitrary non$-$negative integer, and a program made up of orders of one of two types.

The first type has the form:

The interpretation is that at point $\backslash ($ m $\backslash )$ in the program, register $\backslash ($ r$\_\{$j$\}\backslash )$ is incremented by one, and execution proceeds to point $\backslash ($ n $\backslash )$ in the program.

The second type of order has the form:

The interpretation is that at point $\backslash ($ m $\backslash )$ in the program, register $\backslash ($ r$\_\{$j$\}\backslash )$ is decremented if it contains a positive integer, and execution proceeds to point $\backslash ($ n $\backslash )$ in the program. If register $\backslash ($ r$\_\{$j$\}\backslash )$ is zero, then execution simply proceeds to point $\backslash ($ p $\backslash )$ in the program.

The program for the Minsky machine consists of a collection of such orders, in a form shown in the figure below. The starting point and all possible halting points for the program are conventionally labeled zero. The above program takes the contents of register $\backslash ($ r$\_\{1\}\backslash )$ and adds them to register $\backslash ($ r$\_\{2\}\backslash ),$ while decrementing $\backslash ($ r$\_\{1\}\backslash )$ to zero.

Create a Minsky machine that computes the square of a natural number.