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@@ -12,10 +12,26 @@ leaving the gate.}
 
 \subsection*{1.b}
 \emph{Consider the timed automaton in figure 1 of the paper ”Timed Automata” by
-Rajeev Alur. Suppose initially we have a zone $(s0, [0 \leq x \leq 4, 0 \leq y
+Rajeev Alur. Suppose initially we have a zone $(s0, [0\leq x\leq 4, 0\leq y
 \leq 3])$. Give the zone after a sequence a.b and show the intermediate steps
 in the derivation.}
 
+We define:\\
+$e_0=\langle s_0, a, \emptyset, [x:=0] s_1\rangle$ and\\
+$e_1=\langle s_1, a, \emptyset, [y:=0] s_2\rangle$\\
+
+And we derive:\\
+\begin{align*}
+	succ(e_1, succ(e_0, [0\leq x\leq 4, 0\leq y])) =&
+		succ(e_1, ((([0\leq x\leq 4, 0\leq y]\wedge\emptyset)\Uparrow)\wedge\emptyset\wedge [x<1])[x:=0])\\
+	=& succ(e_1, (([0\leq x\leq 4, 0\leq y]\Uparrow)\wedge\emptyset\wedge [x<1])[x:=0])\\
+	=& succ(e_1, [0\leq x<1, 0\leq y][x:=0])\\
+	=& succ(e_1, [x=0, 0\leq y])\\
+	=& ((([x=0, 0\leq y]\wedge [x<1])\Uparrow)\wedge [x<1]\wedge [x<1])[y:=0]\\
+	=& (([0\leq x<1, 0\leq y]\Uparrow)\wedge [x<1]\wedge [x<1])[y:=0]\\
+	=& [0\leq x<1, y=0]
+\end{align*}
+
 \subsection*{1.c}
 \emph{Consider the timed automaton in figure 1 of the paper \emph{Timed
 Automata} by Rajeev Alur. Give the zone automaton of the timed automaton, with