Green's Relation for Semigroup with many D-classes
(Artificial Example)

1. Generators
   a : [1, 0, 2, 3, 4]
   b : [0, 1, 3, 2, 4]
   c : [0, 0, 1, 2, 3]
   

2. Elements
   Elements : 48
   

   I	Representation	Map
   	a	[1, 0, 2, 3, 4]
   	b	[0, 1, 3, 2, 4]
   	c	[0, 0, 1, 2, 3]
   *	a.a	[0, 1, 2, 3, 4]
   	b.a	[1, 0, 3, 2, 4]
   	c.a	[1, 1, 0, 2, 3]
   	c.b	[0, 0, 1, 3, 2]
   	b.c	[0, 0, 2, 1, 3]
   	c.c	[0, 0, 0, 1, 2]
   	c.b.a	[1, 1, 0, 3, 2]
   	b.c.a	[1, 1, 2, 0, 3]
   	c.c.a	[1, 1, 1, 0, 2]
   	b.c.b	[0, 0, 3, 1, 2]
   	c.c.b	[0, 0, 0, 1, 3]
   	c.b.c	[0, 0, 0, 2, 1]
   	b.c.c	[0, 0, 1, 0, 2]
   	c.c.c	[0, 0, 0, 0, 1]
   	b.c.b.a	[1, 1, 3, 0, 2]
   	c.c.b.a	[1, 1, 1, 0, 3]
   	c.b.c.a	[1, 1, 1, 2, 0]
   	b.c.c.a	[1, 1, 0, 1, 2]
   	c.c.c.a	[1, 1, 1, 1, 0]
   	c.b.c.b	[0, 0, 0, 3, 1]
   	b.c.c.b	[0, 0, 1, 0, 3]
   	b.c.b.c	[0, 0, 2, 0, 1]
   	c.c.b.c	[0, 0, 0, 0, 2]
   	c.b.c.c	[0, 0, 0, 1, 0]
   *	c.c.c.c	[0, 0, 0, 0, 0]
   	c.b.c.b.a	[1, 1, 1, 3, 0]
   	b.c.c.b.a	[1, 1, 0, 1, 3]
   	b.c.b.c.a	[1, 1, 2, 1, 0]
   	c.c.b.c.a	[1, 1, 1, 1, 2]
   	c.b.c.c.a	[1, 1, 1, 0, 1]
   *	c.c.c.c.a	[1, 1, 1, 1, 1]
   	b.c.b.c.b	[0, 0, 3, 0, 1]
   	c.c.b.c.b	[0, 0, 0, 0, 3]
   	c.b.c.b.c	[0, 0, 0, 2, 0]
   	b.c.b.c.c	[0, 0, 1, 0, 0]
   	b.c.b.c.b.a	[1, 1, 3, 1, 0]
   	c.c.b.c.b.a	[1, 1, 1, 1, 3]
   	c.b.c.b.c.a	[1, 1, 1, 2, 1]
   	b.c.b.c.c.a	[1, 1, 0, 1, 1]
   *	c.b.c.b.c.b	[0, 0, 0, 3, 0]
   *	b.c.b.c.b.c	[0, 0, 2, 0, 0]
   *	c.b.c.b.c.b.a	[1, 1, 1, 3, 1]
   *	b.c.b.c.b.c.a	[1, 1, 2, 1, 1]
   	b.c.b.c.b.c.b	[0, 0, 3, 0, 0]
   	b.c.b.c.b.c.b.a	[1, 1, 3, 1, 1]

3. D Classes
   D classes : 9, L classes : 27, R classes : 14
   
   • D0
     L classes : 1, R classes : 1, Total : 4 elements, H class : 4 elements
     

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

   • D1
     L classes : 4, R classes : 2, Total : 8 elements, H class : 1 elements
     

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

   • D2
     L classes : 4, R classes : 2, Total : 8 elements, H class : 1 elements
     

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

   • D3
     L classes : 4, R classes : 2, Total : 8 elements, H class : 1 elements
     

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

   • D4
     L classes : 4, R classes : 2, Total : 8 elements, H class : 1 elements
     

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

   • D5
     L classes : 2, R classes : 2, Total : 4 elements, H class : 1 elements
     

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

   • D6
     L classes : 4, R classes : 1, Total : 4 elements, H class : 1 elements
     

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

   • D7
     L classes : 2, R classes : 1, Total : 2 elements, H class : 1 elements
     

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

   • D8
     L classes : 2, R classes : 1, Total : 2 elements, H class : 1 elements
     

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

4. Hierarchy of L & R classes
   
   • Left Classes
     
     • Height: 5
       

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

     • Height: 4
       

       L#	Image	Children	Elements
       1	[0, 1, 2, 3]	5, 11	[1, 1, 0, 2, 3], [1, 1, 2, 0, 3]
       2	[0, 1, 2, 3]	6, 8	[0, 0, 1, 2, 3], [0, 0, 2, 1, 3]
       3	[0, 1, 2, 3]	7, 12	[0, 0, 1, 3, 2], [0, 0, 3, 1, 2]
       4	[0, 1, 2, 3]	9, 10	[1, 1, 0, 3, 2], [1, 1, 3, 0, 2]

     • Height: 3
       

       L#	Image	Children	Elements
       5	[0, 1, 2]	18	[1, 1, 1, 0, 2], [1, 1, 0, 1, 2]
       6	[0, 1, 2]	15	[0, 0, 0, 1, 2], [0, 0, 1, 0, 2]
       7	[0, 1, 3]	15	[0, 0, 0, 1, 3], [0, 0, 1, 0, 3]
       8	[0, 1, 2]	14	[0, 0, 0, 2, 1], [0, 0, 2, 0, 1]
       9	[0, 1, 3]	13	[1, 1, 1, 3, 0], [1, 1, 3, 1, 0]
       10	[0, 1, 3]	18	[1, 1, 1, 0, 3], [1, 1, 0, 1, 3]
       11	[0, 1, 2]	17	[1, 1, 1, 2, 0], [1, 1, 2, 1, 0]
       12	[0, 1, 3]	16	[0, 0, 0, 3, 1], [0, 0, 3, 0, 1]

     • Height: 2
       

       L#	Image	Children	Elements
       13	[1, 3]	23	[1, 1, 1, 3, 1], [1, 1, 3, 1, 1]
       14	[0, 2]	22	[0, 0, 0, 2, 0], [0, 0, 2, 0, 0]
       15	[0, 1]	20	[0, 0, 0, 1, 0], [0, 0, 1, 0, 0]
       16	[0, 3]	21	[0, 0, 0, 3, 0], [0, 0, 3, 0, 0]
       17	[1, 2]	19	[1, 1, 1, 2, 1], [1, 1, 2, 1, 1]
       18	[0, 1]	24	[1, 1, 1, 0, 1], [1, 1, 0, 1, 1]

     • Height: 1
       

       L#	Image	Children	Elements
       19	[1, 2]	26	[1, 1, 1, 1, 2]
       20	[0, 1]	25	[0, 0, 0, 0, 1]
       21	[0, 3]	25	[0, 0, 0, 0, 3]
       22	[0, 2]	25	[0, 0, 0, 0, 2]
       23	[1, 3]	26	[1, 1, 1, 1, 3]
       24	[0, 1]	26	[1, 1, 1, 1, 0]

     • Height: 0
       

       L#	Image	Children	Elements
       25	[0]	-	[0, 0, 0, 0, 0]
       26	[1]	-	[1, 1, 1, 1, 1]

   • Right Classes
     
     • Height: 5
       

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

     • Height: 4
       

       L#	Kernel	Children	Elements
       1	[[0, 1], [2], [3], [4]]	3, 4	[0, 0, 1, 2, 3], [1, 1, 0, 2, 3], [0, 0, 1, 3, 2], [1, 1, 0, 3, 2]
       2	[[0, 1], [2], [3], [4]]	5, 6	[0, 0, 2, 1, 3], [1, 1, 2, 0, 3], [0, 0, 3, 1, 2], [1, 1, 3, 0, 2]

     • Height: 3
       

       L#	Kernel	Children	Elements
       3	[[0, 1, 2], [3], [4]]	8	[0, 0, 0, 1, 2], [1, 1, 1, 0, 2], [0, 0, 0, 1, 3], [1, 1, 1, 0, 3]
       4	[[0, 1, 2], [3], [4]]	9	[0, 0, 0, 2, 1], [1, 1, 1, 2, 0], [0, 0, 0, 3, 1], [1, 1, 1, 3, 0]
       5	[[0, 1, 3], [2], [4]]	8	[0, 0, 1, 0, 2], [1, 1, 0, 1, 2], [0, 0, 1, 0, 3], [1, 1, 0, 1, 3]
       6	[[0, 1, 3], [2], [4]]	7	[0, 0, 2, 0, 1], [1, 1, 2, 1, 0], [0, 0, 3, 0, 1], [1, 1, 3, 1, 0]

     • Height: 2
       

       L#	Kernel	Children	Elements
       7	[[0, 1, 3, 4], [2]]	10	[0, 0, 2, 0, 0], [1, 1, 2, 1, 1], [0, 0, 3, 0, 0], [1, 1, 3, 1, 1]
       8	[[0, 1, 2, 3], [4]]	12	[0, 0, 0, 0, 2], [1, 1, 1, 1, 2], [0, 0, 0, 0, 3], [1, 1, 1, 1, 3]
       9	[[0, 1, 2, 4], [3]]	11	[0, 0, 0, 2, 0], [1, 1, 1, 2, 1], [0, 0, 0, 3, 0], [1, 1, 1, 3, 1]

     • Height: 1
       

       L#	Kernel	Children	Elements
       10	[[0, 1, 3, 4], [2]]	13	[0, 0, 1, 0, 0], [1, 1, 0, 1, 1]
       11	[[0, 1, 2, 4], [3]]	13	[0, 0, 0, 1, 0], [1, 1, 1, 0, 1]
       12	[[0, 1, 2, 3], [4]]	13	[0, 0, 0, 0, 1], [1, 1, 1, 1, 0]

     • Height: 0
       

       L#	Kernel	Children	Elements
       13	[[0, 1, 2, 3, 4]]	-	[0, 0, 0, 0, 0], [1, 1, 1, 1, 1]