YES

After renaming modulo { 0->0, *->1, 1->2, #->3, $->4 }, 
it remains to prove termination of the 7-rule system
{ 0 1 -> 1 2 ,
  2 1 -> 0 3 ,
  3 0 -> 0 3 ,
  3 2 -> 2 3 ,
  3 4 -> 1 4 ,
  3 3 -> 3 ,
  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 1 |
| 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 |
 \   /

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


Applying the dependency pairs transformation.

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


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 0 |
| 0 1 |
 \   /

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


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

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

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

The system is trivially terminating.