YES

After renaming modulo { p->0, s->1, n->2, o->3, m->4, t->5, c->6 }, 
it remains to prove termination of the 15-rule system
{ 0 1 -> 1 ,
  2 1 -> 1 ,
  3 1 -> 1 ,
  3 2 -> 2 3 ,
  3 4 -> 2 3 ,
  2 3 0 -> 3 2 ,
  5 ->= 5 6 2 ,
  0 2 ->= 4 0 ,
  0 4 ->= 4 0 ,
  2 0 ->= 0 2 ,
  6 0 ->= 0 6 ,
  6 4 ->= 4 6 ,
  6 2 ->= 2 6 ,
  6 3 ->= 3 6 ,
  6 3 ->= 3 }


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 0 |
| 0 1 |
 \   /

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


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

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


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

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

The system is trivially terminating.