YES

After renaming modulo { r1->0, a->1, r2->2, l1->3, l2->4, b->5 }, 
it remains to prove termination of the 9-rule system
{ 0 1 -> 1 1 1 0 ,
  2 1 -> 1 1 1 2 ,
  1 3 -> 3 1 1 1 ,
  1 1 4 -> 4 1 1 ,
  0 5 -> 3 5 ,
  2 5 -> 4 1 5 ,
  5 3 -> 5 2 ,
  5 4 -> 5 0 ,
  1 1 -> }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (0,false)->3, (2,true)->4, (2,false)->5, (3,false)->6, (4,false)->7, (5,false)->8, (5,true)->9 },
it remains to prove termination of the 29-rule system
{ 0 1 -> 2 1 1 3 ,
  0 1 -> 2 1 3 ,
  0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 2 1 1 5 ,
  4 1 -> 2 1 5 ,
  4 1 -> 2 5 ,
  4 1 -> 4 ,
  2 6 -> 2 1 1 ,
  2 6 -> 2 1 ,
  2 6 -> 2 ,
  2 1 7 -> 2 1 ,
  2 1 7 -> 2 ,
  0 8 -> 9 ,
  4 8 -> 2 8 ,
  4 8 -> 9 ,
  9 6 -> 9 5 ,
  9 6 -> 4 ,
  9 7 -> 9 3 ,
  9 7 -> 0 ,
  3 1 ->= 1 1 1 3 ,
  5 1 ->= 1 1 1 5 ,
  1 6 ->= 6 1 1 1 ,
  1 1 7 ->= 7 1 1 ,
  3 8 ->= 6 8 ,
  5 8 ->= 7 1 8 ,
  8 6 ->= 8 5 ,
  8 7 ->= 8 3 ,
  1 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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, 
it remains to prove termination of the 27-rule system
{ 0 1 -> 2 1 1 3 ,
  0 1 -> 2 1 3 ,
  0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 2 1 1 5 ,
  4 1 -> 2 1 5 ,
  4 1 -> 2 5 ,
  4 1 -> 4 ,
  2 6 -> 2 1 1 ,
  2 6 -> 2 1 ,
  2 6 -> 2 ,
  2 1 7 -> 2 1 ,
  2 1 7 -> 2 ,
  4 8 -> 2 8 ,
  9 6 -> 9 5 ,
  9 6 -> 4 ,
  9 7 -> 9 3 ,
  9 7 -> 0 ,
  3 1 ->= 1 1 1 3 ,
  5 1 ->= 1 1 1 5 ,
  1 6 ->= 6 1 1 1 ,
  1 1 7 ->= 7 1 1 ,
  3 8 ->= 6 8 ,
  5 8 ->= 7 1 8 ,
  8 6 ->= 8 5 ,
  8 7 ->= 8 3 ,
  1 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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 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, 8->8, 9->9 }, 
it remains to prove termination of the 25-rule system
{ 0 1 -> 2 1 1 3 ,
  0 1 -> 2 1 3 ,
  0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 2 1 1 5 ,
  4 1 -> 2 1 5 ,
  4 1 -> 2 5 ,
  4 1 -> 4 ,
  2 6 -> 2 1 1 ,
  2 6 -> 2 1 ,
  2 6 -> 2 ,
  2 1 7 -> 2 1 ,
  2 1 7 -> 2 ,
  4 8 -> 2 8 ,
  9 6 -> 9 5 ,
  9 7 -> 9 3 ,
  3 1 ->= 1 1 1 3 ,
  5 1 ->= 1 1 1 5 ,
  1 6 ->= 6 1 1 1 ,
  1 1 7 ->= 7 1 1 ,
  3 8 ->= 6 8 ,
  5 8 ->= 7 1 8 ,
  8 6 ->= 8 5 ,
  8 7 ->= 8 3 ,
  1 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 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 4->2, 2->3, 6->4, 7->5, 9->6, 5->7, 3->8, 8->9 }, 
it remains to prove termination of the 18-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 -> 3 1 1 ,
  3 4 -> 3 1 ,
  3 4 -> 3 ,
  3 1 5 -> 3 1 ,
  3 1 5 -> 3 ,
  6 4 -> 6 7 ,
  6 5 -> 6 8 ,
  8 1 ->= 1 1 1 8 ,
  7 1 ->= 1 1 1 7 ,
  1 4 ->= 4 1 1 1 ,
  1 1 5 ->= 5 1 1 ,
  8 9 ->= 4 9 ,
  7 9 ->= 5 1 9 ,
  9 4 ->= 9 7 ,
  9 5 ->= 9 8 ,
  1 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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 6->3, 4->4, 7->5, 5->6, 8->7, 9->8 }, 
it remains to prove termination of the 13-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 -> 3 5 ,
  3 6 -> 3 7 ,
  7 1 ->= 1 1 1 7 ,
  5 1 ->= 1 1 1 5 ,
  1 4 ->= 4 1 1 1 ,
  1 1 6 ->= 6 1 1 ,
  7 8 ->= 4 8 ,
  5 8 ->= 6 1 8 ,
  8 4 ->= 8 5 ,
  8 6 ->= 8 7 ,
  1 1 ->= }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

The system is trivially terminating.