Green's Relation of T4

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

2. Elements
   Elements : 256
   

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

3. D Classes
   D classes : 4, L classes : 15, R classes : 15
   
   • D0
     L classes : 1, R classes : 1, Total : 24 elements, H class : 24 elements
     

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

   • D1
     L classes : 4, R classes : 6, Total : 144 elements, H class : 6 elements
     

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

   • D2
     L classes : 6, R classes : 7, Total : 84 elements, H class : 2 elements
     

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

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

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

4. Hierarchy of L & R classes
   
   • Left Classes
     
     • Height: 3
       

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

     • Height: 2
       

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

     • Height: 1
       

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

     • Height: 0
       

       L#	Image	Children	Elements
       11	[1]	-	[1, 1, 1, 1]
       12	[2]	-	[2, 2, 2, 2]
       13	[0]	-	[0, 0, 0, 0]
       14	[3]	-	[3, 3, 3, 3]

   • Right Classes
     
     • Height: 3
       

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

     • Height: 2
       

       L#	Kernel	Children	Elements
       1	[[0], [1, 2], [3]]	8, 9, 12	[2, 0, 0, 1], [2, 1, 1, 0], [3, 1, 1, 2], [1, 0, 0, 2], [3, 0, 0, 2], [0, 1, 1, 2], [3, 2, 2, 1], [0, 2, 2, 3], [2, 1, 1, 3], [3, 2, 2, 0], [1, 2, 2, 3], [2, 0, 0, 3], [0, 1, 1, 3], [0, 3, 3, 2], [1, 3, 3, 0], [1, 0, 0, 3], [1, 3, 3, 2], [0, 3, 3, 1], [2, 3, 3, 0], [3, 1, 1, 0], [1, 2, 2, 0], [0, 2, 2, 1], [2, 3, 3, 1], [3, 0, 0, 1]
       2	[[0, 3], [1], [2]]	7, 8, 10	[0, 1, 2, 0], [1, 0, 2, 1], [1, 2, 3, 1], [0, 2, 3, 0], [2, 1, 3, 2], [2, 3, 0, 2], [2, 0, 3, 2], [2, 3, 1, 2], [1, 3, 0, 1], [3, 2, 0, 3], [3, 0, 1, 3], [1, 2, 0, 1], [0, 3, 1, 0], [3, 2, 1, 3], [3, 1, 0, 3], [0, 2, 1, 0], [3, 0, 2, 3], [2, 0, 1, 2], [2, 1, 0, 2], [3, 1, 2, 3], [0, 3, 2, 0], [1, 3, 2, 1], [0, 1, 3, 0], [1, 0, 3, 1]
       3	[[0, 1], [2], [3]]	7, 9, 11	[0, 0, 1, 2], [1, 1, 0, 2], [1, 1, 2, 3], [0, 0, 2, 3], [2, 2, 1, 3], [2, 2, 3, 0], [2, 2, 0, 3], [2, 2, 3, 1], [1, 1, 3, 0], [3, 3, 2, 0], [3, 3, 0, 1], [1, 1, 2, 0], [0, 0, 3, 1], [3, 3, 2, 1], [3, 3, 1, 0], [0, 0, 2, 1], [3, 3, 0, 2], [2, 2, 0, 1], [2, 2, 1, 0], [3, 3, 1, 2], [0, 0, 3, 2], [1, 1, 3, 2], [0, 0, 1, 3], [1, 1, 0, 3]
       4	[[0], [1, 3], [2]]	7, 12, 13	[1, 0, 2, 0], [0, 1, 2, 1], [2, 1, 3, 1], [2, 0, 3, 0], [1, 2, 3, 2], [3, 2, 0, 2], [2, 0, 1, 0], [0, 2, 3, 2], [3, 2, 1, 2], [2, 1, 0, 1], [3, 1, 0, 1], [2, 3, 0, 3], [0, 3, 1, 3], [3, 1, 2, 1], [3, 0, 1, 0], [2, 3, 1, 3], [1, 3, 0, 3], [3, 0, 2, 0], [0, 3, 2, 3], [0, 2, 1, 2], [1, 2, 0, 2], [1, 3, 2, 3], [0, 1, 3, 1], [1, 0, 3, 0]
       5	[[0], [1], [2, 3]]	10, 11, 12	[1, 2, 0, 0], [0, 2, 1, 1], [2, 3, 1, 1], [2, 1, 0, 0], [2, 3, 0, 0], [2, 0, 1, 1], [1, 3, 2, 2], [3, 0, 2, 2], [3, 2, 1, 1], [0, 3, 2, 2], [3, 1, 2, 2], [3, 2, 0, 0], [3, 0, 1, 1], [2, 0, 3, 3], [0, 1, 3, 3], [3, 1, 0, 0], [2, 1, 3, 3], [1, 0, 3, 3], [0, 2, 3, 3], [0, 3, 1, 1], [0, 1, 2, 2], [1, 0, 2, 2], [1, 2, 3, 3], [1, 3, 0, 0]
       6	[[0, 2], [1], [3]]	9, 10, 13	[0, 2, 0, 1], [1, 2, 1, 0], [1, 3, 1, 2], [0, 3, 0, 2], [2, 3, 2, 1], [2, 0, 2, 3], [0, 1, 0, 2], [2, 3, 2, 0], [2, 1, 2, 3], [1, 0, 1, 2], [1, 0, 1, 3], [3, 0, 3, 2], [3, 1, 3, 0], [1, 2, 1, 3], [0, 1, 0, 3], [3, 1, 3, 2], [3, 0, 3, 1], [0, 2, 0, 3], [3, 2, 3, 0], [2, 1, 2, 0], [2, 0, 2, 1], [3, 2, 3, 1], [1, 3, 1, 0], [0, 3, 0, 1]

     • Height: 1
       

       L#	Kernel	Children	Elements
       7	[[0, 1, 3], [2]]	14	[0, 0, 1, 0], [1, 1, 0, 1], [1, 1, 2, 1], [0, 0, 2, 0], [2, 2, 1, 2], [2, 2, 3, 2], [2, 2, 0, 2], [1, 1, 3, 1], [3, 3, 2, 3], [3, 3, 0, 3], [0, 0, 3, 0], [3, 3, 1, 3]
       8	[[0, 3], [1, 2]]	14	[2, 0, 0, 2], [2, 1, 1, 2], [3, 1, 1, 3], [1, 0, 0, 1], [3, 0, 0, 3], [0, 1, 1, 0], [3, 2, 2, 3], [0, 2, 2, 0], [1, 2, 2, 1], [0, 3, 3, 0], [1, 3, 3, 1], [2, 3, 3, 2]
       9	[[0, 1, 2], [3]]	14	[0, 0, 0, 1], [1, 1, 1, 0], [1, 1, 1, 2], [0, 0, 0, 2], [2, 2, 2, 1], [2, 2, 2, 3], [2, 2, 2, 0], [1, 1, 1, 3], [3, 3, 3, 2], [3, 3, 3, 0], [0, 0, 0, 3], [3, 3, 3, 1]
       10	[[0, 2, 3], [1]]	14	[0, 1, 0, 0], [1, 0, 1, 1], [1, 2, 1, 1], [0, 2, 0, 0], [2, 1, 2, 2], [2, 3, 2, 2], [2, 0, 2, 2], [1, 3, 1, 1], [3, 2, 3, 3], [3, 0, 3, 3], [0, 3, 0, 0], [3, 1, 3, 3]
       11	[[0, 1], [2, 3]]	14	[2, 2, 0, 0], [2, 2, 1, 1], [3, 3, 1, 1], [1, 1, 0, 0], [3, 3, 0, 0], [0, 0, 1, 1], [3, 3, 2, 2], [0, 0, 2, 2], [1, 1, 2, 2], [0, 0, 3, 3], [1, 1, 3, 3], [2, 2, 3, 3]
       12	[[0], [1, 2, 3]]	14	[1, 0, 0, 0], [0, 1, 1, 1], [2, 1, 1, 1], [2, 0, 0, 0], [1, 2, 2, 2], [3, 2, 2, 2], [0, 2, 2, 2], [3, 1, 1, 1], [2, 3, 3, 3], [0, 3, 3, 3], [3, 0, 0, 0], [1, 3, 3, 3]
       13	[[0, 2], [1, 3]]	14	[0, 2, 0, 2], [1, 2, 1, 2], [1, 3, 1, 3], [0, 1, 0, 1], [2, 0, 2, 0], [0, 3, 0, 3], [1, 0, 1, 0], [2, 1, 2, 1], [2, 3, 2, 3], [3, 1, 3, 1], [3, 0, 3, 0], [3, 2, 3, 2]

     • Height: 0
       

       L#	Kernel	Children	Elements
       14	[[0, 1, 2, 3]]	-	[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3]