YES

After renaming modulo { a->0, b->1 }, 
it remains to prove termination of the 1-rule system
{ 0 1 0 1 0 1 0 0 0 0 0 -> 0 0 0 0 0 0 1 0 1 0 1 0 1 }


The system was reversed.

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


Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019].

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3, (2,true)->4, (3,false)->5, (4,false)->6 },
it remains to prove termination of the 41-rule system
{ 0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 2 3 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 2 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 4 2 3 2 3 2 3 1 1 1 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 4 2 3 2 3 1 1 1 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 4 2 3 1 1 1 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 4 1 1 1 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 0 1 1 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 0 1 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 0 1 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 0 1 5 ,
  0 1 1 1 1 2 3 2 3 2 3 5 -> 0 5 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 2 3 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 2 ,
  1 1 1 1 1 2 3 2 3 2 3 1 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 1 ,
  1 1 1 1 1 2 3 2 3 2 3 2 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 2 ,
  1 1 1 1 1 2 3 2 3 2 3 5 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 5 ,
  3 1 1 1 1 2 3 2 3 2 3 2 ->= 6 3 2 3 2 3 2 3 1 1 1 1 1 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5 }, 
it remains to prove termination of the 31-rule system
{ 0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 2 3 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 2 3 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 4 1 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 2 ,
  4 1 1 1 1 2 3 2 3 2 3 2 -> 0 2 ,
  1 1 1 1 1 2 3 2 3 2 3 1 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 1 ,
  1 1 1 1 1 2 3 2 3 2 3 2 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 2 ,
  3 1 1 1 1 2 3 2 3 2 3 2 ->= 5 3 2 3 2 3 2 3 1 1 1 1 1 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4 }, 
it remains to prove termination of the 21-rule system
{ 0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 2 3 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 2 3 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 4 1 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 2 3 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 4 1 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 2 ,
  1 1 1 1 1 2 3 2 3 2 3 1 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 1 ,
  1 1 1 1 1 2 3 2 3 2 3 2 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 2 }


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 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, 
it remains to prove termination of the 13-rule system
{ 0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 1 ,
  0 1 1 1 1 2 3 2 3 2 3 1 -> 0 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 1 2 ,
  0 1 1 1 1 2 3 2 3 2 3 2 -> 0 2 ,
  1 1 1 1 1 2 3 2 3 2 3 1 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 1 ,
  1 1 1 1 1 2 3 2 3 2 3 2 ->= 2 3 2 3 2 3 2 3 1 1 1 1 1 2 }


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 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

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

The system is trivially terminating.