YES

After renaming modulo { r->0, e->1, w->2, i->3, t->4 }, 
it remains to prove termination of the 7-rule system
{ 0 1 -> 2 0 ,
  3 4 -> 1 0 ,
  1 2 -> 0 3 ,
  4 1 -> 0 1 ,
  2 0 -> 3 4 ,
  1 0 -> 1 2 ,
  0 3 4 1 0 -> 1 2 0 3 4 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 2 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 3 |
| 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 -> 2 0 ,
  3 4 -> 1 0 ,
  1 2 -> 0 3 ,
  2 0 -> 3 4 ,
  0 3 4 1 0 -> 1 2 0 3 4 1 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (0,false)->3, (3,true)->4, (4,false)->5, (1,true)->6, (2,false)->7, (3,false)->8 },
it remains to prove termination of the 17-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  4 5 -> 6 3 ,
  4 5 -> 0 ,
  6 7 -> 0 8 ,
  6 7 -> 4 ,
  2 3 -> 4 5 ,
  0 8 5 1 3 -> 6 7 3 8 5 1 ,
  0 8 5 1 3 -> 2 3 8 5 1 ,
  0 8 5 1 3 -> 0 8 5 1 ,
  0 8 5 1 3 -> 4 5 1 ,
  0 8 5 1 3 -> 6 ,
  3 1 ->= 7 3 ,
  8 5 ->= 1 3 ,
  1 7 ->= 3 8 ,
  7 3 ->= 8 5 ,
  3 8 5 1 3 ->= 1 7 3 8 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 2 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, 
it remains to prove termination of the 10-rule system
{ 0 1 -> 2 3 ,
  4 5 -> 6 3 ,
  6 7 -> 0 8 ,
  2 3 -> 4 5 ,
  0 8 5 1 3 -> 6 7 3 8 5 1 ,
  3 1 ->= 7 3 ,
  8 5 ->= 1 3 ,
  1 7 ->= 3 8 ,
  7 3 ->= 8 5 ,
  3 8 5 1 3 ->= 1 7 3 8 5 1 }


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 1 0 0 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 1 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /

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

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

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

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

The system is trivially terminating.