YES

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


The system was reversed.

After renaming modulo { 1->0, 0->1, 2->2, 3->3 }, 
it remains to prove termination of the 4-rule system
{ 0 1 -> 1 0 ,
  2 1 -> 1 2 ,
  3 1 2 -> 1 3 ,
  1 3 0 -> 3 2 2 0 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,true)->6, (3,false)->7 },
it remains to prove termination of the 15-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 1 -> 2 5 ,
  4 1 -> 4 ,
  6 1 5 -> 2 7 ,
  6 1 5 -> 6 ,
  2 7 3 -> 6 5 5 3 1 ,
  2 7 3 -> 4 5 3 1 ,
  2 7 3 -> 4 3 1 ,
  2 7 3 -> 0 1 ,
  2 7 3 -> 2 ,
  3 1 ->= 1 3 ,
  5 1 ->= 1 5 ,
  7 1 5 ->= 1 7 ,
  1 7 3 ->= 7 5 5 3 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 1 |
| 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 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

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

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

The system is trivially terminating.