Green's Relation of Semigroup for accepting Binary-coded Quaternary

1. Generators
   B : [1, 0, 3, 2, 4]
   dot : [2, 4, 4, 4, 4]
   

2. Elements
   Elements : 7
   

   I	Representation	Map
   	B	[1, 0, 3, 2, 4]
   	dot	[2, 4, 4, 4, 4]
   *	B.B	[0, 1, 2, 3, 4]
   	dot.B	[3, 4, 4, 4, 4]
   	B.dot	[4, 2, 4, 4, 4]
   *	dot.dot	[4, 4, 4, 4, 4]
   	B.dot.B	[4, 3, 4, 4, 4]

3. D Classes
   D classes : 3, L classes : 4, R classes : 4
   
   • D0
     L classes : 1, R classes : 1, Total : 2 elements, H class : 2 elements
     

     R L	[0, 1, 2, 3, 4]
     [[0], [1], [2], [3], [4]]	[0, 1, 2, 3, 4]*, [1, 0, 3, 2, 4]

   • D1
     L classes : 2, R classes : 2, Total : 4 elements, H class : 1 elements
     

     R L	[2, 4]	[3, 4]
     [[0], [1, 2, 3, 4]]	[2, 4, 4, 4, 4]	[3, 4, 4, 4, 4]
     [[0, 2, 3, 4], [1]]	[4, 2, 4, 4, 4]	[4, 3, 4, 4, 4]

   • D2
     L classes : 1, R classes : 1, Total : 1 elements, H class : 1 elements
     

     R L	[4]
     [[0, 1, 2, 3, 4]]	[4, 4, 4, 4, 4]*

4. Hierarchy of L & R classes
   
   • Left Classes
     
     • Height: 2
       

       L#	Image	Children	Elements
       0	[0, 1, 2, 3, 4]	1, 2	[1, 0, 3, 2, 4], [0, 1, 2, 3, 4]

     • Height: 1
       

       L#	Image	Children	Elements
       1	[2, 4]	3	[2, 4, 4, 4, 4], [4, 2, 4, 4, 4]
       2	[3, 4]	3	[3, 4, 4, 4, 4], [4, 3, 4, 4, 4]

     • Height: 0
       

       L#	Image	Children	Elements
       3	[4]	-	[4, 4, 4, 4, 4]

   • Right Classes
     
     • Height: 2
       

       L#	Kernel	Children	Elements
       0	[[0], [1], [2], [3], [4]]	1, 2	[1, 0, 3, 2, 4], [0, 1, 2, 3, 4]

     • Height: 1
       

       L#	Kernel	Children	Elements
       1	[[0], [1, 2, 3, 4]]	3	[2, 4, 4, 4, 4], [3, 4, 4, 4, 4]
       2	[[0, 2, 3, 4], [1]]	3	[4, 2, 4, 4, 4], [4, 3, 4, 4, 4]

     • Height: 0
       

       L#	Kernel	Children	Elements
       3	[[0, 1, 2, 3, 4]]	-	[4, 4, 4, 4, 4]