A vessel where some chemical reaction takes place can be cooled by inserting two different rods, each with different cooling capacities. Only one rod can be inserted at a certain time. The vessel can be in three different states:

no rods: then the temperature $T$ evolves according to the differential equation $T^{\text{'}}=0\mathrm{.}1T-10\mathrm{.}0$

with rod$1$: equation is $T^{\text{'}}=0\mathrm{.}1T-11\mathrm{.}2$

with rod$2$: equation is $T^{\text{'}}=0\mathrm{.}1T-12\mathrm{.}0($so rod$2$ cools better than $\{$:rod$1).$

A rod will be inserted if the temperature reaches $110$ degrees. A rod that is in the vessel will be removed from the vessel if the temperature is between $102$ and $105$ degrees. When a rod is removed, it cannot be used for $20$ time units. Initial temperature is $102$ degrees. The objective is to keep the temperature between $102$ and $110$ degrees. If the temperature is going up to $110$ degrees but no rod is yet available, the system goes into a state Overheating.

$2.$a Specify the system in UPPAAL. Show that unfortunately it may reach state Overheating. What is the chance this happens within $100$ time units?