Lecture 008
We can turn the following into a control graph to check validity.
0 \leq x \leq 3 \to [\text{ while } \ (x > 1) \ x := x - 2](x \leq x \leq 1)

Control Graph of Loop Program
\begin{align*}
R &: 0\leq x \leq 3, \lnot(x > 1) \models 0 \leq x \leq 1 \tag{valid}\\
LR &: 0 \leq x \leq 3, x > 1, x' = x - 2, \lnot(x' > 1) \models 0 \leq x' \leq 1 \tag{valid}\\
LL &: 0 \leq x \leq 3, x > 1, x' = x - 2, x' > 1 \models 0 \leq x' \leq 3 \tag{contradiction}\\
\end{align*}