$1.$ Write an example code that contains a common sub$-$expression $($Programme$-1).$ Rewrite the code to eliminate the common subexpression $($Programe$-2).$ Code both these programs in Python programming language. Run these programs on your computer$/$laptop and measure the execution time, and memory usage, and compare them.

$2.$ Briefly illustrate the process of using inference rules for type checking with examples.