$3.$ Theoretical Pipeline Performance Metrics: $(5$ points$)$ A single issue, scalar, in$-$order $13$ stage pipeline computing system operates at a clock rate of $2$GHz$.$ a$.$ Without the use of any compiler optimizations what is the ideal, theoretical CPO that can be achieved on this processor? Explain your answer in words. Clearly state any additional assumptions you make in your analysis. b$.$ Give the maximum compiler optimizations for scheduling, loop unrolling, out$-$oforder execution $--$ what is the ideal, theoretical CPO that can be achieved on this processor? Explain you answer in words. Clearly state any additional assumptions you make in your analysis.