YES

After renaming modulo { q0->0, 0->1, 0'->2, q1->3, 1'->4, 1->5, q2->6, q3->7, b->8, q4->9 }, 
it remains to prove termination of the 16-rule system
{ 0 1 -> 2 3 ,
  3 1 -> 1 3 ,
  3 4 -> 4 3 ,
  1 3 5 -> 6 1 4 ,
  2 3 5 -> 6 2 4 ,
  4 3 5 -> 6 4 4 ,
  1 6 1 -> 6 1 1 ,
  2 6 1 -> 6 2 1 ,
  4 6 1 -> 6 4 1 ,
  1 6 4 -> 6 1 4 ,
  2 6 4 -> 6 2 4 ,
  4 6 4 -> 6 4 4 ,
  6 2 -> 2 0 ,
  0 4 -> 4 7 ,
  7 4 -> 4 7 ,
  7 8 -> 8 9 }


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 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 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 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

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


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 1 |
| 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 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (0,false)->3, (2,false)->4, (2,true)->5, (3,false)->6, (4,true)->7, (5,true)->8, (5,false)->9, (4,false)->10 },
it remains to prove termination of the 27-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  0 4 -> 5 3 ,
  0 4 -> 0 ,
  2 6 1 -> 2 1 ,
  2 6 1 -> 2 ,
  7 6 1 -> 7 1 ,
  7 6 1 -> 2 ,
  5 6 1 -> 5 1 ,
  5 6 1 -> 2 ,
  2 6 4 -> 2 4 ,
  2 6 4 -> 5 ,
  7 6 4 -> 7 4 ,
  7 6 4 -> 5 ,
  5 6 4 -> 5 4 ,
  5 6 4 -> 5 ,
  8 4 -> 5 9 ,
  8 4 -> 8 ,
  3 1 ->= 1 3 ,
  3 4 ->= 4 3 ,
  1 6 1 ->= 6 1 1 ,
  10 6 1 ->= 6 10 1 ,
  4 6 1 ->= 6 4 1 ,
  1 6 4 ->= 6 1 4 ,
  10 6 4 ->= 6 10 4 ,
  4 6 4 ->= 6 4 4 ,
  9 4 ->= 4 9 }


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 0 |
| 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 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.