Min_number = ( 0 ) ; Max_number = ( 5 )
In original model number_of_states = ( 40 ); number_of_transition = ( 63 ) 

Original Transition
0 --- 1  -> (x)
0 --- 4  -> ((-1)*x+(1))
1 --- 16  -> (p12*p11)
1 --- 17  -> ((-1)*p12*p11+p11)
1 --- 18  -> ((-1)*p12*p11+p12)
1 --- 19  -> (p12*p11-p11-p12+(1))
2 --- 20  -> (p22*p21)
2 --- 21  -> ((-1)*p22*p21+p21)
2 --- 22  -> ((-1)*p22*p21+p22)
2 --- 23  -> (p22*p21-p21-p22+(1))
3 --- 24  -> (p32*p31)
3 --- 25  -> ((-1)*p32*p31+p31)
3 --- 26  -> ((-1)*p32*p31+p32)
3 --- 27  -> (p32*p31-p31-p32+(1))
4 --- 28  -> (p42*p41)
4 --- 29  -> ((-1)*p42*p41+p41)
4 --- 30  -> ((-1)*p42*p41+p42)
4 --- 31  -> (p42*p41-p41-p42+(1))
5 --- 32  -> (p52*p51)
5 --- 33  -> ((-1)*p52*p51+p51)
5 --- 34  -> ((-1)*p52*p51+p52)
5 --- 35  -> (p52*p51-p51-p52+(1))
6 --- 36  -> (p62*p61)
6 --- 37  -> ((-1)*p62*p61+p61)
6 --- 38  -> ((-1)*p62*p61+p62)
6 --- 39  -> (p62*p61-p61-p62+(1))
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 --- 10  -> (1)
11 --- 11  -> (1)
12 --- 12  -> (1)
13 --- 13  -> (1)
14 --- 14  -> (1)
15 --- 0  -> (1)
16 --- 2  -> (1)
17 --- 2  -> (1)
18 --- 2  -> (1)
19 --- 14  -> (1)
20 --- 7  -> (1)
21 --- 7  -> (1)
22 --- 7  -> (1)
23 --- 13  -> (1)
24 --- 6  -> (1)
25 --- 6  -> (1)
26 --- 6  -> (1)
27 --- 12  -> (1)
28 --- 8  -> (1)
29 --- 8  -> (1)
30 --- 8  -> (1)
31 --- 11  -> (1)
32 --- 6  -> (1)
33 --- 6  -> (1)
34 --- 6  -> (1)
35 --- 10  -> (1)
36 --- 15  -> (1)
37 --- 15  -> (1)
38 --- 15  -> (1)
39 --- 9  -> (1)


In New Model number of states = ( 43 ); number of transition = ( 68 ) 

New transition
0 --- 1  -> (x)
0 --- 4  -> ((-1)*x+(1))
1 --- 16  -> (p12*p11)
1 --- 17  -> ((-1)*p12*p11+p11)
1 --- 18  -> ((-1)*p12*p11+p12)
1 --- 19  -> (p12*p11-p11-p12+(1))
2 --- 20  -> (p22*p21)
2 --- 21  -> ((-1)*p22*p21+p21)
2 --- 22  -> ((-1)*p22*p21+p22)
3 --- 24  -> (p32*p31)
3 --- 25  -> ((-1)*p32*p31+p31)
3 --- 26  -> ((-1)*p32*p31+p32)
3 --- 27  -> (p32*p31-p31-p32+(1))
6 --- 36  -> (p62*p61)
6 --- 37  -> ((-1)*p62*p61+p61)
6 --- 38  -> ((-1)*p62*p61+p62)
6 --- 39  -> (p62*p61-p61-p62+(1))
7 --- 1  -> (y2)
7 --- 5  -> (y1)
9 --- 9  -> (1)
10 --- 10  -> (1)
11 --- 11  -> (1)
12 --- 12  -> (1)
13 --- 13  -> (1)
14 --- 14  -> (1)
15 --- 0  -> (1)
16 --- 2  -> (1)
17 --- 2  -> (1)
18 --- 2  -> (1)
19 --- 14  -> (1)
20 --- 7  -> (1)
21 --- 7  -> (1)
22 --- 7  -> (1)
23 --- 13  -> (1)
24 --- 6  -> (1)
25 --- 6  -> (1)
26 --- 6  -> (1)
27 --- 12  -> (1)
28 --- 8  -> (1)
29 --- 8  -> (1)
30 --- 8  -> (1)
31 --- 11  -> (1)
32 --- 6  -> (1)
33 --- 6  -> (1)
34 --- 6  -> (1)
35 --- 10  -> (1)
36 --- 15  -> (1)
37 --- 15  -> (1)
38 --- 15  -> (1)
39 --- 9  -> (1)
8 --- 28  -> ( ((-1)*z1-z2+(1)) ) * ( (p42*p41) )
8 --- 29  -> ( ((-1)*z1-z2+(1)) ) * ( ((-1)*p42*p41+p41) )
8 --- 30  -> ( ((-1)*z1-z2+(1)) ) * ( ((-1)*p42*p41+p42) )
8 --- 31  -> ( ((-1)*z1-z2+(1)) ) * ( (p42*p41-p41-p42+(1)) )
7 --- 40  -> ((-1)*y1-y2+(1))
40 --- 3  -> 1
8 --- 32  -> ( (z1) ) * ( (p52*p51) )
8 --- 33  -> ( (z1) ) * ( ((-1)*p52*p51+p51) )
8 --- 34  -> ( (z1) ) * ( ((-1)*p52*p51+p52) )
8 --- 35  -> ( (z1) ) * ( (p52*p51-p51-p52+(1)) )
2 --- 41  -> (p22*p21-p21-p22+(1))
41 --- 23  -> 1
8 --- 42  -> (z2)
42 --- 0  -> 1
4 --- 8  ->   ( (p42*p41) ) * ( (1) ) + ( ((-1)*p42*p41+p41) ) * ( (1) )  + ( ((-1)*p42*p41+p42) ) * ( (1) ) 
4 --- 11  -> ( (p42*p41-p41-p42+(1)) ) * ( (1) )
5 --- 6  ->   ( (p52*p51) ) * ( (1) ) + ( ((-1)*p52*p51+p51) ) * ( (1) )  + ( ((-1)*p52*p51+p52) ) * ( (1) ) 
5 --- 10  -> ( (p52*p51-p51-p52+(1)) ) * ( (1) )


State--Fragment Number--visited--startingPoint--endingPoint
   0          1          true        true          false
   1          1          true        false          false
   2          1          true        false          false
   3          5          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          6          true        true          true
   10          7          true        true          true
   11          8          true        true          true
   12          9          true        true          true
   13          10          true        true          true
   14          11          true        true          true
   15          12          true        true          true
   16          1          true        false          false
   17          1          true        false          false
   18          1          true        false          false
   19          1          true        false          true
   20          1          true        false          false
   21          1          true        false          false
   22          1          true        false          false
   23          4          true        true          true
   24          13          true        true          true
   25          14          true        true          true
   26          15          true        true          true
   27          16          true        true          true
   28          3          true        false          false
   29          3          true        false          false
   30          3          true        false          false
   31          3          true        false          true
   32          3          true        false          true
   33          3          true        false          true
   34          3          true        false          true
   35          3          true        false          true
   36          2          true        false          true
   37          2          true        false          true
   38          2          true        false          true
   39          2          true        false          true
   40          1          true        false          true
   41          1          true        false          true
   42          3          true        false          true

This is transition in Fragment (1) 
    [0, 1]  (x)
    [0, 4]  ((-1)*x+(1))
    [1, 16]  (p12*p11)
    [1, 17]  ((-1)*p12*p11+p11)
    [1, 18]  ((-1)*p12*p11+p12)
    [1, 19]  (p12*p11-p11-p12+(1))
    [2, 20]  (p22*p21)
    [2, 21]  ((-1)*p22*p21+p21)
    [2, 22]  ((-1)*p22*p21+p22)
    [7, 1]  (y2)
    [7, 5]  (y1)
    [16, 2]  (1)
    [17, 2]  (1)
    [18, 2]  (1)
    [20, 7]  (1)
    [21, 7]  (1)
    [22, 7]  (1)
    [7, 40]  ((-1)*y1-y2+(1))
    [2, 41]  (p22*p21-p21-p22+(1))
    [4, 4]  1
    [5, 5]  1
    [19, 19]  1
    [40, 40]  1
    [41, 41]  1

This is transition in Fragment (2) 
    [6, 36]  (p62*p61)
    [6, 37]  ((-1)*p62*p61+p61)
    [6, 38]  ((-1)*p62*p61+p62)
    [6, 39]  (p62*p61-p61-p62+(1))
    [36, 36]  1
    [37, 37]  1
    [38, 38]  1
    [39, 39]  1

This is transition in Fragment (3) 
    [28, 8]  (1)
    [29, 8]  (1)
    [30, 8]  (1)
    [8, 28]  ( ((-1)*z1-z2+(1)) ) * ( (p42*p41) )
    [8, 29]  ( ((-1)*z1-z2+(1)) ) * ( ((-1)*p42*p41+p41) )
    [8, 30]  ( ((-1)*z1-z2+(1)) ) * ( ((-1)*p42*p41+p42) )
    [8, 31]  ( ((-1)*z1-z2+(1)) ) * ( (p42*p41-p41-p42+(1)) )
    [8, 32]  ( (z1) ) * ( (p52*p51) )
    [8, 33]  ( (z1) ) * ( ((-1)*p52*p51+p51) )
    [8, 34]  ( (z1) ) * ( ((-1)*p52*p51+p52) )
    [8, 35]  ( (z1) ) * ( (p52*p51-p51-p52+(1)) )
    [8, 42]  (z2)
    [31, 31]  1
    [32, 32]  1
    [33, 33]  1
    [34, 34]  1
    [35, 35]  1
    [42, 42]  1

This is transition in Fragment (4) 
    [23, 23]  1

This is transition in Fragment (5) 
    [3, 3]  1

This is transition in Fragment (6) 
    [9, 9]  1

This is transition in Fragment (7) 
    [10, 10]  1

This is transition in Fragment (8) 
    [11, 11]  1

This is transition in Fragment (9) 
    [12, 12]  1

This is transition in Fragment (10) 
    [13, 13]  1

This is transition in Fragment (11) 
    [14, 14]  1

This is transition in Fragment (12) 
    [15, 15]  1

This is transition in Fragment (13) 
    [24, 24]  1

This is transition in Fragment (14) 
    [25, 25]  1

This is transition in Fragment (15) 
    [26, 26]  1

This is transition in Fragment (16) 
    [27, 27]  1

This is transition for abstract model 
    [3, 24]  (p32*p31)
    [3, 25]  ((-1)*p32*p31+p31)
    [3, 26]  ((-1)*p32*p31+p32)
    [3, 27]  (p32*p31-p31-p32+(1))
    [9, 9]  (1)
    [10, 10]  (1)
    [11, 11]  (1)
    [12, 12]  (1)
    [13, 13]  (1)
    [14, 14]  (1)
    [15, 0]  (1)
    [19, 14]  ( (1) ) * ( prob_f1_s19 )
    [23, 13]  (1)
    [24, 6]  (1)
    [25, 6]  (1)
    [26, 6]  (1)
    [27, 12]  (1)
    [31, 11]  ( (1) ) * ( prob_f3_s31 )
    [32, 6]  ( (1) ) * ( prob_f3_s32 )
    [33, 6]  ( (1) ) * ( prob_f3_s33 )
    [34, 6]  ( (1) ) * ( prob_f3_s34 )
    [35, 10]  ( (1) ) * ( prob_f3_s35 )
    [36, 15]  ( (1) ) * ( prob_f2_s36 )
    [37, 15]  ( (1) ) * ( prob_f2_s37 )
    [38, 15]  ( (1) ) * ( prob_f2_s38 )
    [39, 9]  ( (1) ) * ( prob_f2_s39 )
    [40, 3]  ( 1 ) * ( prob_f1_s40 )
    [41, 23]  ( 1 ) * ( prob_f1_s41 )
    [42, 0]  ( 1 ) * ( prob_f3_s42 )
    [4, 8]  (   ( (p42*p41) ) * ( (1) ) + ( ((-1)*p42*p41+p41) ) * ( (1) )  + ( ((-1)*p42*p41+p42) ) * ( (1) )  ) * ( prob_f1_s4 )
    [4, 11]  ( ( (p42*p41-p41-p42+(1)) ) * ( (1) ) ) * ( prob_f1_s4 )
    [5, 6]  (   ( (p52*p51) ) * ( (1) ) + ( ((-1)*p52*p51+p51) ) * ( (1) )  + ( ((-1)*p52*p51+p52) ) * ( (1) )  ) * ( prob_f1_s5 )
    [5, 10]  ( ( (p52*p51-p51-p52+(1)) ) * ( (1) ) ) * ( prob_f1_s5 )
****************************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 = ((p12*p11)); 
P1_1_4 = (((-1)*p12*p11+p11)); 
P1_1_5 = (((-1)*p12*p11+p12)); 
P1_1_6 = ((p12*p11-p11-p12+(1))); 
P1_2_7 = ((p22*p21)); 
P1_2_8 = (((-1)*p22*p21+p21)); 
P1_2_9 = (((-1)*p22*p21+p22)); 
P1_2_19 = ((p22*p21-p21-p22+(1))); 
P1_7_10 = ((y2)); 
P1_7_11 = ((y1)); 
P1_7_18 = (((-1)*y1-y2+(1))); 
P1_16_12 = ((1)); 
P1_17_13 = ((1)); 
P1_18_14 = ((1)); 
P1_20_15 = ((1)); 
P1_21_16 = ((1)); 
P1_22_17 = ((1)); 

prob_f1_s4  =( (P1_0_2)/(1)); 
prob_f1_s5  =( (-1 * ((P1_0_1) * (P1_1_5*P1_2_9*P1_7_11+P1_1_5*P1_2_8*P1_7_11+P1_1_4*P1_2_9*P1_7_11+P1_1_3*P1_2_7*P1_7_11+P1_1_3*P1_2_8*P1_7_11+P1_1_4*P1_2_7*P1_7_11+P1_1_4*P1_2_8*P1_7_11+P1_1_3*P1_2_9*P1_7_11+P1_1_5*P1_2_7*P1_7_11)))/(P1_1_5*P1_2_9*P1_7_10+P1_1_3*P1_2_9*P1_7_10+P1_1_4*P1_2_9*P1_7_10+P1_1_5*P1_2_8*P1_7_10+P1_1_3*P1_2_8*P1_7_10+P1_1_4*P1_2_8*P1_7_10+P1_1_5*P1_2_7*P1_7_10+P1_1_3*P1_2_7*P1_7_10+P1_1_4*P1_2_7*P1_7_10+(-1))); 
prob_f1_s19  =( (-1 * ((P1_0_1) * (P1_1_6)))/(P1_1_5*P1_2_9*P1_7_10+P1_1_3*P1_2_9*P1_7_10+P1_1_4*P1_2_9*P1_7_10+P1_1_5*P1_2_8*P1_7_10+P1_1_3*P1_2_8*P1_7_10+P1_1_4*P1_2_8*P1_7_10+P1_1_5*P1_2_7*P1_7_10+P1_1_3*P1_2_7*P1_7_10+P1_1_4*P1_2_7*P1_7_10+(-1))); 
prob_f1_s40  =( (-1 * ((P1_0_1) * (P1_1_5*P1_2_9*P1_7_18+P1_1_5*P1_2_8*P1_7_18+P1_1_4*P1_2_9*P1_7_18+P1_1_3*P1_2_7*P1_7_18+P1_1_3*P1_2_8*P1_7_18+P1_1_4*P1_2_7*P1_7_18+P1_1_4*P1_2_8*P1_7_18+P1_1_3*P1_2_9*P1_7_18+P1_1_5*P1_2_7*P1_7_18)))/(P1_1_5*P1_2_9*P1_7_10+P1_1_3*P1_2_9*P1_7_10+P1_1_4*P1_2_9*P1_7_10+P1_1_5*P1_2_8*P1_7_10+P1_1_3*P1_2_8*P1_7_10+P1_1_4*P1_2_8*P1_7_10+P1_1_5*P1_2_7*P1_7_10+P1_1_3*P1_2_7*P1_7_10+P1_1_4*P1_2_7*P1_7_10+(-1))); 
prob_f1_s41  =( (-1 * ((P1_0_1) * (P1_1_5*P1_2_19+P1_1_3*P1_2_19+P1_1_4*P1_2_19)))/(P1_1_5*P1_2_9*P1_7_10+P1_1_3*P1_2_9*P1_7_10+P1_1_4*P1_2_9*P1_7_10+P1_1_5*P1_2_8*P1_7_10+P1_1_3*P1_2_8*P1_7_10+P1_1_4*P1_2_8*P1_7_10+P1_1_5*P1_2_7*P1_7_10+P1_1_3*P1_2_7*P1_7_10+P1_1_4*P1_2_7*P1_7_10+(-1))); 
P2_6_1 = ((p62*p61)); 
P2_6_2 = (((-1)*p62*p61+p61)); 
P2_6_3 = (((-1)*p62*p61+p62)); 
P2_6_4 = ((p62*p61-p61-p62+(1))); 

prob_f2_s36  =( (P2_6_1)/(1)); 
prob_f2_s37  =( (P2_6_2)/(1)); 
prob_f2_s38  =( (P2_6_3)/(1)); 
prob_f2_s39  =( (P2_6_4)/(1)); 
P3_8_4 = (( ((-1)*z1-z2+(1)) ) * ( (p42*p41) )); 
P3_8_5 = (( ((-1)*z1-z2+(1)) ) * ( ((-1)*p42*p41+p41) )); 
P3_8_6 = (( ((-1)*z1-z2+(1)) ) * ( ((-1)*p42*p41+p42) )); 
P3_8_7 = (( ((-1)*z1-z2+(1)) ) * ( (p42*p41-p41-p42+(1)) )); 
P3_8_8 = (( (z1) ) * ( (p52*p51) )); 
P3_8_9 = (( (z1) ) * ( ((-1)*p52*p51+p51) )); 
P3_8_10 = (( (z1) ) * ( ((-1)*p52*p51+p52) )); 
P3_8_11 = (( (z1) ) * ( (p52*p51-p51-p52+(1)) )); 
P3_8_12 = ((z2)); 
P3_28_1 = ((1)); 
P3_29_2 = ((1)); 
P3_30_3 = ((1)); 

prob_f3_s31  =( (-1 * (P3_8_7))/(P3_8_6+P3_8_5+P3_8_4+(-1))); 
prob_f3_s32  =( (-1 * (P3_8_8))/(P3_8_6+P3_8_5+P3_8_4+(-1))); 
prob_f3_s33  =( (-1 * (P3_8_9))/(P3_8_6+P3_8_5+P3_8_4+(-1))); 
prob_f3_s34  =( (-1 * (P3_8_10))/(P3_8_6+P3_8_5+P3_8_4+(-1))); 
prob_f3_s35  =( (-1 * (P3_8_11))/(P3_8_6+P3_8_5+P3_8_4+(-1))); 
prob_f3_s42  =( (-1 * (P3_8_12))/(P3_8_6+P3_8_5+P3_8_4+(-1))); 
PX_0_12 = (( (1) ) * ( prob_f1_s19 )); 
PX_0_23 = (( 1 ) * ( prob_f1_s40 ));
PX_0_24 = (( 1 ) * ( prob_f1_s41 ));
PX_0_26 = ((   ( (p42*p41) ) * ( (1) ) + ( ((-1)*p42*p41+p41) ) * ( (1) )  + ( ((-1)*p42*p41+p42) ) * ( (1) )  ) * ( prob_f1_s4 ));
PX_0_27 = (( ( (p42*p41-p41-p42+(1)) ) * ( (1) ) ) * ( prob_f1_s4 ));
PX_0_28 = ((   ( (p52*p51) ) * ( (1) ) + ( ((-1)*p52*p51+p51) ) * ( (1) )  + ( ((-1)*p52*p51+p52) ) * ( (1) )  ) * ( prob_f1_s5 ));
PX_0_29 = (( ( (p52*p51-p51-p52+(1)) ) * ( (1) ) ) * ( prob_f1_s5 ));
PX_1_21 = (  ( (1) ) * ( prob_f2_s36 ) + ( (1) ) * ( prob_f2_s37 )  + ( (1) ) * ( prob_f2_s38 ) ); 
PX_1_22 = (( (1) ) * ( prob_f2_s39 ));
PX_2_18 = (( (1) ) * ( prob_f3_s31 )); 
PX_2_19 = (  ( (1) ) * ( prob_f3_s32 ) + ( (1) ) * ( prob_f3_s33 )  + ( (1) ) * ( prob_f3_s34 ) );
PX_2_20 = (( (1) ) * ( prob_f3_s35 ));
PX_2_25 = (( 1 ) * ( prob_f3_s42 ));
PX_3_13 = ((1)); 
PX_4_1 = ((p32*p31)); 
PX_4_2 = (((-1)*p32*p31+p31));
PX_4_3 = (((-1)*p32*p31+p32));
PX_4_4 = ((p32*p31-p31-p32+(1)));
PX_5_5 = ((1)); 
PX_6_6 = ((1)); 
PX_7_7 = ((1)); 
PX_8_8 = ((1)); 
PX_9_9 = ((1)); 
PX_10_10 = ((1)); 
PX_11_11 = ((1)); 
PX_12_14 = ((1)); 
PX_13_15 = ((1)); 
PX_14_16 = ((1)); 
PX_15_17 = ((1)); 

Output_abstract_model =( (-1 * ((PX_1_21) * (PX_0_26*PX_2_19+PX_0_28)))/(PX_0_26*PX_2_25+(-1))); 
