0   1
--------------
   0|   0   0
   1|   0   0
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   0
   1|   0   1
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   0
   1|   1   0
(1*0)*1 = 0  but   1*(0*1) = 1

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   1
   1|   0   0
(1*0)*1 = 1  but   1*(0*1) = 0

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   0
   1|   0   0
(0*0)*1 = 0  but   0*(0*1) = 1

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   0
   1|   1   1
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   1
   1|   0   1
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   0
   1|   0   1
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   1
   1|   1   0
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   0
   1|   1   0
(0*0)*0 = 1  but   0*(0*0) = 0

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   1
   1|   0   0
(0*0)*0 = 0  but   0*(0*0) = 1

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   0   1
   1|   1   1
Semigroup

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   0
   1|   1   1
(0*0)*0 = 1  but   0*(0*0) = 0

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   1
   1|   0   1
(0*0)*0 = 0  but   0*(0*0) = 1

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   1
   1|   1   0
(0*0)*1 = 0  but   0*(0*1) = 1

~~~~~~~~~~~~~~~~~~~~

        0   1
--------------
   0|   1   1
   1|   1   1
Semigroup

~~~~~~~~~~~~~~~~~~~~