YES

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


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 7 |
| 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 9 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

After renaming modulo {  }, 
it remains to prove termination of the 0-rule system
{ }

The system is trivially terminating.