/media/sda-magnetic/david/Dok-15-2023-11-27/fernuni-hagen/cs-i-ii/old-cs-2-01/2021-12-13-uebungen/synthese0003.txt

        b a x   b a y
0       0 0 0   1 0 1
1       0 0 1   0 1 0
2       0 1 0   1 1 0
3       0 1 1   0 0 1
4       1 0 0   1 1 1
5       1 0 1   0 1 1
6       1 1 0   1 1 0
7       1 1 1   0 1 1


        b a x   b
0       0 0 0   1
1       0 0 1   0
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   0
6       1 1 0   1
7       1 1 1   0

        b a x   a
0       0 0 0   0
1       0 0 1   1
2       0 1 0   1
3       0 1 1   0
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
1       0 0 1   0
2       0 1 0   0
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   0
7       1 1 1   1




        b a x   b
0       0 0 0   1
2       0 1 0   1
4       1 0 0   1
6       1 1 0   1

        b a x   a
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
5       1 0 1   1
6       1 1 0   1
7       1 1 1   1

        b a x   y
0       0 0 0   1
3       0 1 1   1
4       1 0 0   1
5       1 0 1   1
7       1 1 1   1



        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1

        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1

        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1




        b a x   b
Gruppe 0:
0       0 0 0   1
Gruppe 1:
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
6       1 1 0   1

0;2     0 - 0
0;4     - 0 0
2;6     - 1 0
4;6     1 - 0

0;2     0 - 0
4;6     1 - 0
0;4     - 0 0
2;6     - 1 0

0;2;4;6     - - 0

b := not x


        b a x   a
Gruppe 1:
1       0 0 1   1
2       0 1 0   1
4       1 0 0   1
Gruppe 2:
5       1 0 1   1
6       1 1 0   1
Gruppe 3:
7       1 1 1   1


1;5     - 0 1
2;6     - 1 0
4;5     1 0 -
4;6     1 - 0
5;7     1 - 1
6;7     1 1 -


Gruppe 1:
1;5     - 0 1
2;6     - 1 0

Gruppe 1:
4;5     1 0 -
Gruppe 2:
6;7     1 1 -

4;5;6;7 1 - -

Gruppe 1:
4;6     1 - 0
Gruppe 2:
5;7     1 - 1

1;4         - 0 1
2;6         - 1 0
4;5;6;7     1 - - 

            1   2   4   5   6   7
1;4         *       *
2;6             *           *
4;5;6;7             *   *   *   *

a := (not a and x) or (a and not x) or b



        b a x   y
Gruppe 0:
0       0 0 0   1
Gruppe 1:
4       1 0 0   1
Gruppe 2:
3       0 1 1   1
5       1 0 1   1
Gruppe 3:
7       1 1 1   1

0;4     - 0 0 
4;5     1 0 -
3;7     - 1 1 
5;7     1 - 1

 
4;5     1 0 -
3;7     - 1 1 
0;4     - 0 0
5;7     1 - 1

            0   3   4   5   7
4;5                 *   *
3;7             *           *
0;4         *       *
5;7                     *   *

            0   3   4   5   7
4;5                 *   *
3;7             *           *
0;4         *       *

y := (b and not a) or (a and x) or (not a and not x) 


b := not x
a := (not a and x) or (a and not x) or b
y := (b and not a) or (a and x) or (not a and not x)