Consider the control system block diagram given in Figure (a). The loop transfer function $G(s) \: H(s)$ does not have any pole on the $j \omega$-axis. The counterclockwise contour with infinite radius, as shown in Figure (b), encircles two poles of $G(s) \: H(s)$. Choose the correct statement from the following options for closed loop stability of the system.
- The locus of $G(s) H(s)$ should encircle the origin twice in the counterclockwise direction
- The locus of $1+G(s) H(s)$ should encircle the origin twice in the clockwise direction
- The locus of $G(s) H(s)$ should encircle the $-1+j 0$ point twice in the counterclockwise direction
- The locus of $1+G(s) H(s)$ should encircle the $-1+j 0$ point twice in the clockwise direction
