Consider the following process definition.

$U={?}_{\text{d}\text{e}\text{f}}^{\text{d}\text{e}\text{f}}a.V,x={?}^{\text{d}\text{e}\text{f}}a*b.Y,Z={?}^{\text{d}\text{e}\text{f}}U+x$

$V={?}^{\text{d}\text{e}\text{f}}b.V+b.a.UY={?}^{\text{d}\text{e}\text{f}}b.Y+a.x,$

$($a$)$ Draw a labelled transition system for the above process definition. Label every state with the process

expression representing that state.

$($b$)$ Explain how the states U$,$ X and Z differ from each other in the behaviour that they exhibit.