There are two concurrent processes P$1$ and P$2$ sharing variables X and Y on a single CPU that has a single core.

P$1$

while $($true$)\{$

X $=$ X $+1$;

wait$($sync$\_$Y$)$;

X$=$ Y $+2$;

signal$($sync$\_$X$)$;

store$($X$)$;

$\}$

P$2$

while $($true$)\{$

Y $=2*$ Y;

signal$($sync$\_$Y$)$;

store$($Y$)$;

transfer$($Y$)$;

wait$($sync$\_$X$)$;

Y $=$ X $+$ Y;

$\}$

Which one of the following statements about the execution sequence of P$1\text{'}$s $"$X $=$ Y $+2$;$"$ and P$2\text{'}$s $"$Y $=2*$ Y;$"$ is correct?