The following assembly code snippet performs operations on two registers, R$1$ and R$2,$ in a hypothetical CPU architecture. Analyze the code and answer the questions below.

MOV R$1,$ #$10$ ;Load immediate value $10$ into R$1$

MOV R$2,$ #$5$ ;Load immediate value $5$ into R$2$

ADD R$1,$ R$1,$ R$2$ ;Add the values in R$1$ and R$2,$ store the result in R$1$

SUB R$2,$ R$1,$ #$3$ ; Subtract $3$ from the value in R$1,$ store the result in R$2$

MUL R$1,$ R$2,$ #$2$ ;Multiply the value in R$2$ by $2,$ store the result in R$1$

$-$ Interpret and Trace Register Values:

After each instruction executes, determine the contents of registers R$1$ and R$2.$ Show your work step$-$by$-$step for each instruction.

$-$ Final Register Values:

What are the final values in R$1$ and R$2$ after all instructions have executed? Explain the sequence of operations that led to these results.

$-$ Alternative Code Analysis:

Rewrite the code to achieve the same final values in R$1$ and R$2$ but using only three instructions. Describe how your new code achieves the same result in a more efficient way.

$-$ Understanding CPU Operation

Based on the operations used, identify which type of CPU instructions $($e$.$g$.,$ arithmetic, immediate, etc.$)$ are represented in the code. Briefly explain how each type of instruction works within the CPU.