Explain in detail with diagram

$($Asynchronous Processes$)$ We expect you to explain your answers $($for example by displaying execution traces of the process$).$ Consider the following asynchronous process that has the following internal tasks:

nat $x=0$; $y=0$; $z=0$;

$T1$ : $(y=2)x$:$=(x+1)mod3$; $y$:$=0$; $z$:$=0$

$T2$ : true $y$ :$=(y+1)mod3$

$T3$ : $(y=1)z$:$=(z+1)mod3$; $y$:$=0$; $x$:$=0$

$T4$ : $(z=1)x$ :$=2$;

$($a$)$ Can there be an execution where $x+y=4?$ If yes, what is it$?$ If

no$,$ why not?

$($b$)$ Can there be an execution where $x+y+z=6?$ If yes, what is

it$?$ If no$,$ why not?

$($c$)$ How many distinct states are reachable from the initial state?

$($d$)$ We will now redesign the asynchronous process such that it is

impossible to reach a state where $x+y+z=5,$ subject to:

$1.$ You can change the guard of just one task.

$2.$ You cannot change anything else $($updates$,$ other guards, initialization, etc.$)$

$3.$ Your new process must have executions reaching a state where $x+y+z=3.$