YES

After renaming modulo { a12->0, a13->1, a14->2, a15->3, a16->4, a23->5, a24->6, a25->7, a26->8, a34->9, a35->10, a36->11, a45->12, a46->13, a56->14 }, 
it remains to prove termination of the 35-rule system
{ 0 0 -> ,
  1 1 -> ,
  2 2 -> ,
  3 3 -> ,
  4 4 -> ,
  5 5 -> ,
  6 6 -> ,
  7 7 -> ,
  8 8 -> ,
  9 9 -> ,
  10 10 -> ,
  11 11 -> ,
  12 12 -> ,
  13 13 -> ,
  14 14 -> ,
  1 -> 0 5 0 ,
  2 -> 0 5 9 5 0 ,
  3 -> 0 5 9 12 9 5 0 ,
  4 -> 0 5 9 12 14 12 9 5 0 ,
  6 -> 5 9 5 ,
  7 -> 5 9 12 9 5 ,
  8 -> 5 9 12 14 12 9 5 ,
  10 -> 9 12 9 ,
  11 -> 9 12 14 12 9 ,
  13 -> 12 14 12 ,
  0 5 0 5 0 5 -> ,
  5 9 5 9 5 9 -> ,
  9 12 9 12 9 12 -> ,
  12 14 12 14 12 14 -> ,
  0 9 -> 9 0 ,
  0 12 -> 12 0 ,
  0 14 -> 14 0 ,
  5 12 -> 12 5 ,
  5 14 -> 14 5 ,
  9 14 -> 14 9 }


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 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 5->1, 9->2, 12->3, 14->4 }, 
it remains to prove termination of the 15-rule system
{ 0 0 -> ,
  1 1 -> ,
  2 2 -> ,
  3 3 -> ,
  4 4 -> ,
  0 1 0 1 0 1 -> ,
  1 2 1 2 1 2 -> ,
  2 3 2 3 2 3 -> ,
  3 4 3 4 3 4 -> ,
  0 2 -> 2 0 ,
  0 3 -> 3 0 ,
  0 4 -> 4 0 ,
  1 3 -> 3 1 ,
  1 4 -> 4 1 ,
  2 4 -> 4 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 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (0,false)->3, (2,false)->4, (3,false)->5, (4,true)->6, (4,false)->7 },
it remains to prove termination of the 13-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  0 4 -> 0 ,
  0 5 -> 0 ,
  6 4 -> 6 ,
  6 5 -> 6 ,
  2 5 -> 2 ,
  3 1 ->= 1 3 ,
  3 4 ->= 4 3 ,
  3 5 ->= 5 3 ,
  7 4 ->= 4 7 ,
  7 5 ->= 5 7 ,
  1 5 ->= 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 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 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.