Computation of the ND simulation according to the algorithm in the
lecture notes (note the definition of ND-simulation and the algorithm
for computing it must be written on the exam solution, also all
tuple deletions must be briefly justified).


R_0  

(t1,s1q1)
(t1,s1q2)
%removed (t1,s1q3) since t1 final and s1q3 not final
(t1,s2q1)
(t1,s2q2)
%removed (t1,s2q3) since t1 final and s2,q3 not final

(t2,s1q1)
(t2,s1q2)
(t2,s1q3)
(t2,s2q1)
(t2,s2q2)
(t2,s2q3)


R_1

(t1,s1q1)
(t1,s1q2)
%removed (t1,s1q3)
(t1,s2q1)
(t1,s2q2)  
%removed (t1,s2q3)

(t2,s1q1)
(t2,s1q2)
(t2,s1q3)
(t2,s2q1)
remove (t2,s2q2) since t2 can do b going to t1, s2q2 can do b going to s2q3
                            but (t1,s2q3) is not in R_0.
(t2,s2q3) 

R_2

(t1,s1q1)
remove (t1,s1q2) since t1 does a going to t2, s1q2 does a 
                           going to s2q2 but  (t2,s2q2) is not in R_1 
%removed (t1,s1q3)
(t1,s2q1) 
(t1,s2q2)  
%removed (t1,s2q3)

(t2,s1q1)
(t2,s1q2)
(t2,s1q3)
(t2,s2q1)
%removed (t2,s2q2)
(t2,s2q3)


R_3

(t1,s1q1)
%removed (t1,s1q2)
%removed (t1,s1q3)
(t1,s2q1) 
(t1,s2q2)  
%removed (t1,s2q3)

(t2,s1q1)
(t2,s1q2)
(t2,s1q3)
(t2,s2q1)
%removed (t2,s2q2)
(t2,s2q3)

At R_3 we cannot eliminate any tuple from the relation: i.e, R_3 is the
result of the algorithm (the greatest simulation relation).



Now, on the basis of the greatest simulation relation, we can
compute the output function of the orchestrator generator - see
lecture notes (note such output function must be written on the exam
solution):

W(t1,s1q1,a) = {1,2}
W(t1,s2q1,a) = {1}
W(t1,s2q2,a) = {1}

W(t2,s1q1,b) = {1,2}
W(t2,s1q2,b) = {1}
W(t2,s1q3,b) = {2}
W(t2,s2q1,b) = {2}
W(t2,s2q3,b) = {2}


Any choice of the index, at each point in time, according to the above
function guarantees a composition.