Min_number = ( 0 ) ; Max_number = ( 5 )
In original model number_of_states = ( 23 ); number_of_transition = ( 46 ) 

Original Transition
0 --- 1  -> (x)
0 --- 4  -> ((-1)*x+(1))
1 --- 21  -> (z11)/(z11+z12)
1 --- 22  -> (z12)/(z11+z12)
2 --- 19  -> (z21)/(z21+z22)
2 --- 20  -> (z22)/(z21+z22)
3 --- 17  -> (z31)/(z31+z32)
3 --- 18  -> (z32)/(z31+z32)
4 --- 15  -> (z41)/(z41+z42)
4 --- 16  -> (z42)/(z41+z42)
5 --- 13  -> (z51)/(z51+z52)
5 --- 14  -> (z52)/(z51+z52)
6 --- 11  -> (z61)/(z61+z62)
6 --- 12  -> (z62)/(z61+z62)
7 --- 1  -> (y2)
7 --- 3  -> ((-1)*y1-y2+(1))
7 --- 5  -> (y1)
8 --- 0  -> (z2)
8 --- 4  -> ((-1)*z1-z2+(1))
8 --- 5  -> (z1)
9 --- 9  -> (1)
10 --- 0  -> (1)
11 --- 9  -> ((-1)*p61+(1))
11 --- 10  -> (p61)
12 --- 9  -> ((-1)*p62+(1))
12 --- 10  -> (p62)
13 --- 6  -> (p51)
13 --- 9  -> ((-1)*p51+(1))
14 --- 6  -> (p52)
14 --- 9  -> ((-1)*p52+(1))
15 --- 8  -> (p41)
15 --- 9  -> ((-1)*p41+(1))
16 --- 8  -> (p42)
16 --- 9  -> ((-1)*p42+(1))
17 --- 6  -> (p31)
17 --- 9  -> ((-1)*p31+(1))
18 --- 6  -> (p32)
18 --- 9  -> ((-1)*p32+(1))
19 --- 7  -> (p21)
19 --- 9  -> ((-1)*p21+(1))
20 --- 7  -> (p22)
20 --- 9  -> ((-1)*p22+(1))
21 --- 2  -> (p11)
21 --- 9  -> ((-1)*p11+(1))
22 --- 2  -> (p12)
22 --- 9  -> ((-1)*p12+(1))


In New Model number of states = ( 31 ); number of transition = ( 56 ) 

New transition
0 --- 1  -> (x)
0 --- 4  -> ((-1)*x+(1))
1 --- 21  -> (z11)/(z11+z12)
1 --- 22  -> (z12)/(z11+z12)
2 --- 19  -> (z21)/(z21+z22)
2 --- 20  -> (z22)/(z21+z22)
3 --- 17  -> (z31)/(z31+z32)
3 --- 18  -> (z32)/(z31+z32)
6 --- 11  -> (z61)/(z61+z62)
6 --- 12  -> (z62)/(z61+z62)
7 --- 1  -> (y2)
7 --- 5  -> (y1)
9 --- 9  -> (1)
10 --- 0  -> (1)
11 --- 9  -> ((-1)*p61+(1))
11 --- 10  -> (p61)
12 --- 9  -> ((-1)*p62+(1))
12 --- 10  -> (p62)
13 --- 6  -> (p51)
13 --- 9  -> ((-1)*p51+(1))
14 --- 6  -> (p52)
14 --- 9  -> ((-1)*p52+(1))
15 --- 8  -> (p41)
16 --- 8  -> (p42)
17 --- 6  -> (p31)
17 --- 9  -> ((-1)*p31+(1))
18 --- 6  -> (p32)
18 --- 9  -> ((-1)*p32+(1))
19 --- 7  -> (p21)
20 --- 7  -> (p22)
21 --- 2  -> (p11)
22 --- 2  -> (p12)
8 --- 15  -> ( ((-1)*z1-z2+(1)) ) * ( (z41)/(z41+z42) )
8 --- 16  -> ( ((-1)*z1-z2+(1)) ) * ( (z42)/(z41+z42) )
7 --- 23  -> ((-1)*y1-y2+(1))
23 --- 3  -> 1
20 --- 24  -> ((-1)*p22+(1))
24 --- 9  -> 1
8 --- 13  -> ( (z1) ) * ( (z51)/(z51+z52) )
8 --- 14  -> ( (z1) ) * ( (z52)/(z51+z52) )
19 --- 25  -> ((-1)*p21+(1))
25 --- 9  -> 1
21 --- 26  -> ((-1)*p11+(1))
26 --- 9  -> 1
22 --- 27  -> ((-1)*p12+(1))
27 --- 9  -> 1
8 --- 28  -> (z2)
28 --- 0  -> 1
4 --- 8  ->  ( (z41)/(z41+z42) ) * ( (p41) ) + ( (z42)/(z41+z42) ) * ( (p42) ) 
4 --- 9  ->  ( (z41)/(z41+z42) ) * ( ((-1)*p41+(1)) ) + ( (z42)/(z41+z42) ) * ( ((-1)*p42+(1)) ) 
5 --- 6  ->  ( (z51)/(z51+z52) ) * ( (p51) ) + ( (z52)/(z51+z52) ) * ( (p52) ) 
5 --- 9  ->  ( (z51)/(z51+z52) ) * ( ((-1)*p51+(1)) ) + ( (z52)/(z51+z52) ) * ( ((-1)*p52+(1)) ) 
15 --- 29  -> ((-1)*p41+(1))
29 --- 9  -> 1
16 --- 30  -> ((-1)*p42+(1))
30 --- 9  -> 1


State--Fragment Number--visited--startingPoint--endingPoint
   0          1          true        true          false
   1          1          true        false          false
   2          1          true        false          false
   3          4          true        true          true
   4          1          true        false          true
   5          1          true        false          true
   6          2          true        true          false
   7          1          true        false          false
   8          3          true        true          false
   9          5          true        true          true
   10          6          true        true          true
   11          2          true        false          true
   12          2          true        false          true
   13          3          true        false          true
   14          3          true        false          true
   15          3          true        false          false
   16          3          true        false          false
   17          7          true        true          true
   18          8          true        true          true
   19          1          true        false          false
   20          1          true        false          false
   21          1          true        false          false
   22          1          true        false          false
   23          1          true        false          true
   24          1          true        false          true
   25          1          true        false          true
   26          1          true        false          true
   27          1          true        false          true
   28          3          true        false          true
   29          3          true        false          true
   30          3          true        false          true

This is transition in Fragment (1) 
    [0, 1]  (x)
    [0, 4]  ((-1)*x+(1))
    [1, 21]  (z11)/(z11+z12)
    [1, 22]  (z12)/(z11+z12)
    [2, 19]  (z21)/(z21+z22)
    [2, 20]  (z22)/(z21+z22)
    [7, 1]  (y2)
    [7, 5]  (y1)
    [19, 7]  (p21)
    [20, 7]  (p22)
    [21, 2]  (p11)
    [22, 2]  (p12)
    [7, 23]  ((-1)*y1-y2+(1))
    [20, 24]  ((-1)*p22+(1))
    [19, 25]  ((-1)*p21+(1))
    [21, 26]  ((-1)*p11+(1))
    [22, 27]  ((-1)*p12+(1))
    [4, 4]  1
    [5, 5]  1
    [23, 23]  1
    [24, 24]  1
    [25, 25]  1
    [26, 26]  1
    [27, 27]  1

This is transition in Fragment (2) 
    [6, 11]  (z61)/(z61+z62)
    [6, 12]  (z62)/(z61+z62)
    [11, 11]  1
    [12, 12]  1

This is transition in Fragment (3) 
    [15, 8]  (p41)
    [16, 8]  (p42)
    [8, 15]  ( ((-1)*z1-z2+(1)) ) * ( (z41)/(z41+z42) )
    [8, 16]  ( ((-1)*z1-z2+(1)) ) * ( (z42)/(z41+z42) )
    [8, 13]  ( (z1) ) * ( (z51)/(z51+z52) )
    [8, 14]  ( (z1) ) * ( (z52)/(z51+z52) )
    [8, 28]  (z2)
    [15, 29]  ((-1)*p41+(1))
    [16, 30]  ((-1)*p42+(1))
    [13, 13]  1
    [14, 14]  1
    [28, 28]  1
    [29, 29]  1
    [30, 30]  1

This is transition in Fragment (4) 
    [3, 3]  1

This is transition in Fragment (5) 
    [9, 9]  1

This is transition in Fragment (6) 
    [10, 10]  1

This is transition in Fragment (7) 
    [17, 17]  1

This is transition in Fragment (8) 
    [18, 18]  1

This is transition for abstract model 
    [3, 17]  (z31)/(z31+z32)
    [3, 18]  (z32)/(z31+z32)
    [9, 9]  (1)
    [10, 0]  (1)
    [11, 9]  ( ((-1)*p61+(1)) ) * ( prob_f2_s11 )
    [11, 10]  ( (p61) ) * ( prob_f2_s11 )
    [12, 9]  ( ((-1)*p62+(1)) ) * ( prob_f2_s12 )
    [12, 10]  ( (p62) ) * ( prob_f2_s12 )
    [13, 6]  ( (p51) ) * ( prob_f3_s13 )
    [13, 9]  ( ((-1)*p51+(1)) ) * ( prob_f3_s13 )
    [14, 6]  ( (p52) ) * ( prob_f3_s14 )
    [14, 9]  ( ((-1)*p52+(1)) ) * ( prob_f3_s14 )
    [17, 6]  (p31)
    [17, 9]  ((-1)*p31+(1))
    [18, 6]  (p32)
    [18, 9]  ((-1)*p32+(1))
    [23, 3]  ( 1 ) * ( prob_f1_s23 )
    [24, 9]  ( 1 ) * ( prob_f1_s24 )
    [25, 9]  ( 1 ) * ( prob_f1_s25 )
    [26, 9]  ( 1 ) * ( prob_f1_s26 )
    [27, 9]  ( 1 ) * ( prob_f1_s27 )
    [28, 0]  ( 1 ) * ( prob_f3_s28 )
    [4, 8]  (  ( (z41)/(z41+z42) ) * ( (p41) ) + ( (z42)/(z41+z42) ) * ( (p42) )  ) * ( prob_f1_s4 )
    [4, 9]  (  ( (z41)/(z41+z42) ) * ( ((-1)*p41+(1)) ) + ( (z42)/(z41+z42) ) * ( ((-1)*p42+(1)) )  ) * ( prob_f1_s4 )
    [5, 6]  (  ( (z51)/(z51+z52) ) * ( (p51) ) + ( (z52)/(z51+z52) ) * ( (p52) )  ) * ( prob_f1_s5 )
    [5, 9]  (  ( (z51)/(z51+z52) ) * ( ((-1)*p51+(1)) ) + ( (z52)/(z51+z52) ) * ( ((-1)*p52+(1)) )  ) * ( prob_f1_s5 )
    [29, 9]  ( 1 ) * ( prob_f3_s29 )
    [30, 9]  ( 1 ) * ( prob_f3_s30 )
****************************The expressions start from here; Copying following expressions to MATLAB; Providing values for the parameters needed; Checking the result of <Output_abstract_model> ******
P1_0_1 = ((x)); 
P1_0_2 = (((-1)*x+(1))); 
P1_1_3 = ((z11)/(z11+z12)); 
P1_1_4 = ((z12)/(z11+z12)); 
P1_2_5 = ((z21)/(z21+z22)); 
P1_2_6 = ((z22)/(z21+z22)); 
P1_7_7 = ((y2)); 
P1_7_8 = ((y1)); 
P1_7_13 = (((-1)*y1-y2+(1))); 
P1_19_9 = ((p21)); 
P1_19_15 = (((-1)*p21+(1))); 
P1_20_10 = ((p22)); 
P1_20_14 = (((-1)*p22+(1))); 
P1_21_11 = ((p11)); 
P1_21_16 = (((-1)*p11+(1))); 
P1_22_12 = ((p12)); 
P1_22_17 = (((-1)*p12+(1))); 

prob_f1_s4  =( (P1_0_2)/(1)); 
prob_f1_s5  =( (-1 * ((P1_0_1) * (P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_8+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_8+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_8+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_8)))/(P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_7+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_7+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_7+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_7+(-1))); 
prob_f1_s23  =( (-1 * ((P1_0_1) * (P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_13+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_13+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_13+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_13)))/(P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_7+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_7+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_7+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_7+(-1))); 
prob_f1_s24  =( (-1 * ((P1_0_1) * (P1_1_4*P1_22_12*P1_2_6*P1_20_14+P1_1_3*P1_21_11*P1_2_6*P1_20_14)))/(P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_7+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_7+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_7+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_7+(-1))); 
prob_f1_s25  =( (-1 * ((P1_0_1) * (P1_1_4*P1_22_12*P1_2_5*P1_19_15+P1_1_3*P1_21_11*P1_2_5*P1_19_15)))/(P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_7+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_7+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_7+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_7+(-1))); 
prob_f1_s26  =( (-1 * ((P1_0_1) * (P1_1_3*P1_21_16)))/(P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_7+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_7+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_7+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_7+(-1))); 
prob_f1_s27  =( (-1 * ((P1_0_1) * (P1_1_4*P1_22_17)))/(P1_1_4*P1_22_12*P1_2_6*P1_20_10*P1_7_7+P1_1_3*P1_21_11*P1_2_6*P1_20_10*P1_7_7+P1_1_4*P1_22_12*P1_2_5*P1_19_9*P1_7_7+P1_1_3*P1_21_11*P1_2_5*P1_19_9*P1_7_7+(-1))); 
P2_6_1 = ((z61)/(z61+z62)); 
P2_6_2 = ((z62)/(z61+z62)); 

prob_f2_s11  =( (P2_6_1)/(1)); 
prob_f2_s12  =( (P2_6_2)/(1)); 
P3_8_3 = (( ((-1)*z1-z2+(1)) ) * ( (z41)/(z41+z42) )); 
P3_8_4 = (( ((-1)*z1-z2+(1)) ) * ( (z42)/(z41+z42) )); 
P3_8_5 = (( (z1) ) * ( (z51)/(z51+z52) )); 
P3_8_6 = (( (z1) ) * ( (z52)/(z51+z52) )); 
P3_8_7 = ((z2)); 
P3_15_1 = ((p41)); 
P3_15_8 = (((-1)*p41+(1))); 
P3_16_2 = ((p42)); 
P3_16_9 = (((-1)*p42+(1))); 

prob_f3_s13  =( (-1 * (P3_8_5))/(P3_8_4*P3_16_2+P3_8_3*P3_15_1+(-1))); 
prob_f3_s14  =( (-1 * (P3_8_6))/(P3_8_4*P3_16_2+P3_8_3*P3_15_1+(-1))); 
prob_f3_s28  =( (-1 * (P3_8_7))/(P3_8_4*P3_16_2+P3_8_3*P3_15_1+(-1))); 
prob_f3_s29  =( (-1 * (P3_8_3*P3_15_8))/(P3_8_4*P3_16_2+P3_8_3*P3_15_1+(-1))); 
prob_f3_s30  =( (-1 * (P3_8_4*P3_16_9))/(P3_8_4*P3_16_2+P3_8_3*P3_15_1+(-1))); 
PX_0_13 = (( 1 ) * ( prob_f1_s23 )); 
PX_0_14 = (     ( 1 ) * ( prob_f1_s24 ) + ( 1 ) * ( prob_f1_s25 )  + ( 1 ) * ( prob_f1_s26 )  + ( 1 ) * ( prob_f1_s27 )  + (  ( (z41)/(z41+z42) ) * ( ((-1)*p41+(1)) ) + ( (z42)/(z41+z42) ) * ( ((-1)*p42+(1)) )  ) * ( prob_f1_s4 )  + (  ( (z51)/(z51+z52) ) * ( ((-1)*p51+(1)) ) + ( (z52)/(z51+z52) ) * ( ((-1)*p52+(1)) )  ) * ( prob_f1_s5 ) );
PX_0_16 = ((  ( (z41)/(z41+z42) ) * ( (p41) ) + ( (z42)/(z41+z42) ) * ( (p42) )  ) * ( prob_f1_s4 ));
PX_0_17 = ((  ( (z51)/(z51+z52) ) * ( (p51) ) + ( (z52)/(z51+z52) ) * ( (p52) )  ) * ( prob_f1_s5 ));
PX_1_5 = ( ( ((-1)*p61+(1)) ) * ( prob_f2_s11 ) + ( ((-1)*p62+(1)) ) * ( prob_f2_s12 ) ); 
PX_1_6 = ( ( (p61) ) * ( prob_f2_s11 ) + ( (p62) ) * ( prob_f2_s12 ) );
PX_2_7 = ( ( (p51) ) * ( prob_f3_s13 ) + ( (p52) ) * ( prob_f3_s14 ) ); 
PX_2_8 = (   ( ((-1)*p51+(1)) ) * ( prob_f3_s13 ) + ( ((-1)*p52+(1)) ) * ( prob_f3_s14 )  + ( 1 ) * ( prob_f3_s29 )  + ( 1 ) * ( prob_f3_s30 ) );
PX_2_15 = (( 1 ) * ( prob_f3_s28 ));
PX_3_1 = ((z31)/(z31+z32)); 
PX_3_2 = ((z32)/(z31+z32));
PX_4_3 = ((1)); 
PX_5_4 = ((1)); 
PX_6_9 = ((p31)); 
PX_6_10 = (((-1)*p31+(1)));
PX_7_11 = ((p32)); 
PX_7_12 = (((-1)*p32+(1)));

Output_abstract_model =( (-1 * ((PX_1_6) * (PX_0_16*PX_2_7+PX_0_17)))/(PX_0_16*PX_2_15+(-1))); 
