YES

After renaming modulo { a->0, b->1, c->2, C->3, B->4, A->5 }, 
it remains to prove termination of the 12-rule system
{ 0 1 2 -> 2 1 0 ,
  3 4 5 -> 5 4 3 ,
  1 0 3 -> 3 0 1 ,
  2 5 4 -> 4 5 2 ,
  5 2 1 -> 1 2 5 ,
  4 3 0 -> 0 3 4 ,
  0 5 -> ,
  5 0 -> ,
  1 4 -> ,
  4 1 -> ,
  2 3 -> ,
  3 2 -> }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 6-rule system
{ 0 1 2 -> 2 1 0 ,
  3 4 5 -> 5 4 3 ,
  1 0 3 -> 3 0 1 ,
  2 5 4 -> 4 5 2 ,
  5 2 1 -> 1 2 5 ,
  4 3 0 -> 0 3 4 }


The system was reversed.

After renaming modulo { 2->0, 1->1, 0->2, 5->3, 4->4, 3->5 }, 
it remains to prove termination of the 6-rule system
{ 0 1 2 -> 2 1 0 ,
  3 4 5 -> 5 4 3 ,
  5 2 1 -> 1 2 5 ,
  4 3 0 -> 0 3 4 ,
  1 0 3 -> 3 0 1 ,
  2 5 4 -> 4 5 2 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,false)->2, (2,true)->3, (0,false)->4, (1,true)->5, (3,true)->6, (4,false)->7, (5,false)->8, (5,true)->9, (3,false)->10, (4,true)->11 },
it remains to prove termination of the 24-rule system
{ 0 1 2 -> 3 1 4 ,
  0 1 2 -> 5 4 ,
  0 1 2 -> 0 ,
  6 7 8 -> 9 7 10 ,
  6 7 8 -> 11 10 ,
  6 7 8 -> 6 ,
  9 2 1 -> 5 2 8 ,
  9 2 1 -> 3 8 ,
  9 2 1 -> 9 ,
  11 10 4 -> 0 10 7 ,
  11 10 4 -> 6 7 ,
  11 10 4 -> 11 ,
  5 4 10 -> 6 4 1 ,
  5 4 10 -> 0 1 ,
  5 4 10 -> 5 ,
  3 8 7 -> 11 8 2 ,
  3 8 7 -> 9 2 ,
  3 8 7 -> 3 ,
  4 1 2 ->= 2 1 4 ,
  10 7 8 ->= 8 7 10 ,
  8 2 1 ->= 1 2 8 ,
  7 10 4 ->= 4 10 7 ,
  1 4 10 ->= 10 4 1 ,
  2 8 7 ->= 7 8 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 7->6, 8->7, 9->8, 10->9, 5->10, 11->11 }, 
it remains to prove termination of the 12-rule system
{ 0 1 2 -> 3 1 4 ,
  5 6 7 -> 8 6 9 ,
  8 2 1 -> 10 2 7 ,
  11 9 4 -> 0 9 6 ,
  10 4 9 -> 5 4 1 ,
  3 7 6 -> 11 7 2 ,
  4 1 2 ->= 2 1 4 ,
  9 6 7 ->= 7 6 9 ,
  7 2 1 ->= 1 2 7 ,
  6 9 4 ->= 4 9 6 ,
  1 4 9 ->= 9 4 1 ,
  2 7 6 ->= 6 7 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 5->0, 6->1, 7->2, 8->3, 9->4, 2->5, 1->6, 10->7, 11->8, 4->9, 0->10, 3->11 }, 
it remains to prove termination of the 11-rule system
{ 0 1 2 -> 3 1 4 ,
  3 5 6 -> 7 5 2 ,
  8 4 9 -> 10 4 1 ,
  7 9 4 -> 0 9 6 ,
  11 2 1 -> 8 2 5 ,
  9 6 5 ->= 5 6 9 ,
  4 1 2 ->= 2 1 4 ,
  2 5 6 ->= 6 5 2 ,
  1 4 9 ->= 9 4 1 ,
  6 9 4 ->= 4 9 6 ,
  5 2 1 ->= 1 2 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 9->8 }, 
it remains to prove termination of the 9-rule system
{ 0 1 2 -> 3 1 4 ,
  3 5 6 -> 7 5 2 ,
  7 8 4 -> 0 8 6 ,
  8 6 5 ->= 5 6 8 ,
  4 1 2 ->= 2 1 4 ,
  2 5 6 ->= 6 5 2 ,
  1 4 8 ->= 8 4 1 ,
  6 8 4 ->= 4 8 6 ,
  5 2 1 ->= 1 2 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 3->0, 5->1, 6->2, 7->3, 2->4, 8->5, 4->6, 0->7, 1->8 }, 
it remains to prove termination of the 8-rule system
{ 0 1 2 -> 3 1 4 ,
  3 5 6 -> 7 5 2 ,
  5 2 1 ->= 1 2 5 ,
  6 8 4 ->= 4 8 6 ,
  4 1 2 ->= 2 1 4 ,
  8 6 5 ->= 5 6 8 ,
  2 5 6 ->= 6 5 2 ,
  1 4 8 ->= 8 4 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 2->1, 1->2, 6->3, 8->4, 4->5 }, 
it remains to prove termination of the 6-rule system
{ 0 1 2 ->= 2 1 0 ,
  3 4 5 ->= 5 4 3 ,
  5 2 1 ->= 1 2 5 ,
  4 3 0 ->= 0 3 4 ,
  1 0 3 ->= 3 0 1 ,
  2 5 4 ->= 4 5 2 }

The system is trivially terminating.