Min_number = ( 0 ) ; Max_number = ( 15 )
In original model number_of_states = ( 11 ); number_of_transition = ( 22 ) 

Original Transition
0 --- 1  -> (x)
0 --- 4  -> ((-1)*x+1)
1 --- 2  -> (p11)
1 --- 9  -> ((-1)*p11+1)
2 --- 7  -> (p21)
2 --- 9  -> ((-1)*p21+1)
3 --- 6  -> (p31)
3 --- 9  -> ((-1)*p31+1)
4 --- 8  -> (p41)
4 --- 9  -> ((-1)*p41+1)
5 --- 6  -> (p51)
5 --- 9  -> ((-1)*p51+1)
6 --- 9  -> ((-1)*p61+1)
6 --- 10  -> (p61)
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)


In New Model number of states = ( 14 ); number of transition = ( 25 ) 

New transition
0 --- 1  -> (x)
0 --- 4  -> ((-1)*x+1)
1 --- 2  -> (p11)
2 --- 7  -> (p21)
3 --- 6  -> (p31)
3 --- 9  -> ((-1)*p31+1)
4 --- 8  -> (p41)
5 --- 6  -> (p51)
5 --- 9  -> ((-1)*p51+1)
6 --- 9  -> ((-1)*p61+1)
6 --- 10  -> (p61)
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)
1 --- 11  -> ((-1)*p11+1)
11 --- 9  -> 1
4 --- 12  -> ((-1)*p41+1)
12 --- 9  -> 1
2 --- 13  -> ((-1)*p21+1)
13 --- 9  -> 1


State--Fragment Number--visited--startingPoint--endingPoint
   0          1          true        true          false
   1          1          true        false          false
   2          1          true        false          false
   3          1          true        false          true
   4          1          true        false          false
   5          1          true        false          true
   6          2          true        true          true
   7          1          true        false          false
   8          1          true        false          false
   9          3          true        true          true
   10          4          true        true          true
   11          1          true        false          true
   12          1          true        false          true
   13          1          true        false          true

This is transition in Fragment (1) 
    [0, 1]  (x)
    [0, 4]  ((-1)*x+1)
    [1, 2]  (p11)
    [2, 7]  (p21)
    [4, 8]  (p41)
    [7, 1]  (y2)
    [7, 3]  ((-1)*y1-y2+1)
    [7, 5]  (y1)
    [8, 0]  (z2)
    [8, 4]  ((-1)*z1-z2+1)
    [8, 5]  (z1)
    [1, 11]  ((-1)*p11+1)
    [4, 12]  ((-1)*p41+1)
    [2, 13]  ((-1)*p21+1)
    [3, 3]  1
    [5, 5]  1
    [11, 11]  1
    [12, 12]  1
    [13, 13]  1

This is transition in Fragment (2) 
    [6, 6]  1

This is transition in Fragment (3) 
    [9, 9]  1

This is transition in Fragment (4) 
    [10, 10]  1

This is transition for abstract model 
    [3, 6]  ( (p31) ) * ( prob_f1_s3 )
    [3, 9]  ( ((-1)*p31+1) ) * ( prob_f1_s3 )
    [5, 6]  ( (p51) ) * ( prob_f1_s5 )
    [5, 9]  ( ((-1)*p51+1) ) * ( prob_f1_s5 )
    [6, 9]  ((-1)*p61+1)
    [6, 10]  (p61)
    [9, 9]  (1)
    [10, 0]  (1)
    [11, 9]  ( 1 ) * ( prob_f1_s11 )
    [12, 9]  ( 1 ) * ( prob_f1_s12 )
    [13, 9]  ( 1 ) * ( prob_f1_s13 )
P1_0_1 = ((x)); 
P1_0_2 = (((-1)*x+1)); 
P1_1_3 = ((p11)); 
P1_1_12 = (((-1)*p11+1)); 
P1_2_4 = ((p21)); 
P1_2_14 = (((-1)*p21+1)); 
P1_4_5 = ((p41)); 
P1_4_13 = (((-1)*p41+1)); 
P1_7_6 = ((y2)); 
P1_7_7 = (((-1)*y1-y2+1)); 
P1_7_8 = ((y1)); 
P1_8_9 = ((z2)); 
P1_8_10 = (((-1)*z1-z2+1)); 
P1_8_11 = ((z1)); 

prob_f1_s3 =( (-1 * (P1_0_1*P1_1_3*P1_4_5*P1_2_4*P1_8_10*P1_7_7+(-1)*P1_0_1*P1_1_3*P1_2_4*P1_7_7))/((P1_0_2*P1_4_5*P1_8_9+P1_4_5*P1_8_10+(-1)) * (P1_1_3*P1_2_4*P1_7_6+(-1)))); 
prob_f1_s5 =( (-1 * (P1_0_2*P1_1_3*P1_4_5*P1_2_4*P1_8_11*P1_7_6+P1_0_1*P1_1_3*P1_4_5*P1_2_4*P1_8_10*P1_7_8+(-1)*P1_0_1*P1_1_3*P1_2_4*P1_7_8+(-1)*P1_0_2*P1_4_5*P1_8_11))/((P1_0_2*P1_4_5*P1_8_9+P1_4_5*P1_8_10+(-1)) * (P1_1_3*P1_2_4*P1_7_6+(-1)))); 
prob_f1_s11 =( (-1 * (P1_0_1*P1_1_12*P1_4_5*P1_8_10+(-1)*P1_0_1*P1_1_12))/((P1_0_2*P1_4_5*P1_8_9+P1_4_5*P1_8_10+(-1)) * (P1_1_3*P1_2_4*P1_7_6+(-1)))); 
prob_f1_s12 =( (-1 * (P1_0_2*P1_4_13))/(P1_0_2*P1_4_5*P1_8_9+P1_4_5*P1_8_10+(-1))); 
prob_f1_s13 =( (-1 * (P1_0_1*P1_1_3*P1_4_5*P1_2_14*P1_8_10+(-1)*P1_0_1*P1_1_3*P1_2_14))/((P1_0_2*P1_4_5*P1_8_9+P1_4_5*P1_8_10+(-1)) * (P1_1_3*P1_2_4*P1_7_6+(-1)))); 
PX_0_1 = ( ( (p31) ) * ( prob_f1_s3 ) + ( (p51) ) * ( prob_f1_s5 ) ); 
PX_0_2 = (    ( ((-1)*p31+1) ) * ( prob_f1_s3 ) + ( ((-1)*p51+1) ) * ( prob_f1_s5 )  + ( 1 ) * ( prob_f1_s11 )  + ( 1 ) * ( prob_f1_s12 )  + ( 1 ) * ( prob_f1_s13 ) );
PX_1_3 = (((-1)*p61+1)); 
PX_1_4 = ((p61));
PX_2_5 = ((1)); 
PX_3_6 = ((1)); 

Output_abstract_model =( ((PX_0_1) * (PX_1_4))/(1)); 
