Consider the following CCS process definitions:

$P_0,={?}^{\text{d}\text{e}\text{f}},a*P_0+b*P_1+*P_1$

$P_1,={?}^{\text{d}\text{e}\text{f}}a*P_1+*P_2$

$P_2,={?}^{\text{d}\text{e}\text{f}},b*P_0$

$Q_1,={?}^{\text{d}\text{e}\text{f}},a*Q_1+*Q_2$

$Q_2,={?}^{\text{d}\text{e}\text{f}},b*Q_1$

Prove that the relation $B=\{(P_0,Q_1)$;$(P_1,Q_1)$;$(P_2,Q_2)\}$ is a weak$-$bisimulation.