YES

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


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 0 |
| 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 { 2->0, 3->1 }, 
it remains to prove termination of the 1-rule system
{ 0 1 0 1 -> 0 0 1 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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

The system is trivially terminating.