YES

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


The system was reversed.

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

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


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

After renaming modulo { (0,0)->0, (0,1)->1, (1,0)->2, (0,2)->3, (2,1)->4, (1,1)->5, (1,4)->6, (0,4)->7, (3,0)->8, (3,1)->9 },
it remains to prove termination of the 12-rule system
{ 0 1 2 -> 0 3 4 2 0 0 ,
  0 1 5 -> 0 3 4 2 0 1 ,
  0 1 6 -> 0 3 4 2 0 7 ,
  2 1 2 -> 2 3 4 2 0 0 ,
  2 1 5 -> 2 3 4 2 0 1 ,
  2 1 6 -> 2 3 4 2 0 7 ,
  8 1 2 -> 8 3 4 2 0 0 ,
  8 1 5 -> 8 3 4 2 0 1 ,
  8 1 6 -> 8 3 4 2 0 7 ,
  0 3 4 -> 1 ,
  2 3 4 -> 5 ,
  8 3 4 -> 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 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 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,false)->2, (3,false)->3, (4,false)->4, (0,false)->5, (2,true)->6, (5,false)->7, (6,true)->8, (6,false)->9 },
it remains to prove termination of the 29-rule system
{ 0 1 2 -> 0 3 4 2 5 5 ,
  0 1 2 -> 6 5 5 ,
  0 1 2 -> 0 5 ,
  0 1 2 -> 0 ,
  0 1 7 -> 0 3 4 2 5 1 ,
  0 1 7 -> 6 5 1 ,
  0 1 7 -> 0 1 ,
  6 1 2 -> 6 3 4 2 5 5 ,
  6 1 2 -> 6 5 5 ,
  6 1 2 -> 0 5 ,
  6 1 2 -> 0 ,
  6 1 7 -> 6 3 4 2 5 1 ,
  6 1 7 -> 6 5 1 ,
  6 1 7 -> 0 1 ,
  8 1 2 -> 8 3 4 2 5 5 ,
  8 1 2 -> 6 5 5 ,
  8 1 2 -> 0 5 ,
  8 1 2 -> 0 ,
  8 1 7 -> 8 3 4 2 5 1 ,
  8 1 7 -> 6 5 1 ,
  8 1 7 -> 0 1 ,
  5 1 2 ->= 5 3 4 2 5 5 ,
  5 1 7 ->= 5 3 4 2 5 1 ,
  2 1 2 ->= 2 3 4 2 5 5 ,
  2 1 7 ->= 2 3 4 2 5 1 ,
  9 1 2 ->= 9 3 4 2 5 5 ,
  9 1 7 ->= 9 3 4 2 5 1 ,
  5 3 4 ->= 1 ,
  2 3 4 ->= 7 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, 
it remains to prove termination of the 24-rule system
{ 0 1 2 -> 0 3 4 2 5 5 ,
  0 1 2 -> 6 5 5 ,
  0 1 2 -> 0 5 ,
  0 1 2 -> 0 ,
  0 1 7 -> 0 3 4 2 5 1 ,
  0 1 7 -> 6 5 1 ,
  0 1 7 -> 0 1 ,
  6 1 2 -> 6 3 4 2 5 5 ,
  6 1 2 -> 6 5 5 ,
  6 1 2 -> 0 5 ,
  6 1 2 -> 0 ,
  6 1 7 -> 6 3 4 2 5 1 ,
  6 1 7 -> 6 5 1 ,
  6 1 7 -> 0 1 ,
  8 1 2 -> 8 3 4 2 5 5 ,
  8 1 7 -> 8 3 4 2 5 1 ,
  5 1 2 ->= 5 3 4 2 5 5 ,
  5 1 7 ->= 5 3 4 2 5 1 ,
  2 1 2 ->= 2 3 4 2 5 5 ,
  2 1 7 ->= 2 3 4 2 5 1 ,
  9 1 2 ->= 9 3 4 2 5 5 ,
  9 1 7 ->= 9 3 4 2 5 1 ,
  5 3 4 ->= 1 ,
  2 3 4 ->= 7 }


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 1 |
| 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 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 6->7, 8->8, 9->9 }, 
it remains to prove termination of the 14-rule system
{ 0 1 2 -> 0 3 4 2 5 5 ,
  0 1 6 -> 0 3 4 2 5 1 ,
  7 1 2 -> 7 3 4 2 5 5 ,
  7 1 6 -> 7 3 4 2 5 1 ,
  8 1 2 -> 8 3 4 2 5 5 ,
  8 1 6 -> 8 3 4 2 5 1 ,
  5 1 2 ->= 5 3 4 2 5 5 ,
  5 1 6 ->= 5 3 4 2 5 1 ,
  2 1 2 ->= 2 3 4 2 5 5 ,
  2 1 6 ->= 2 3 4 2 5 1 ,
  9 1 2 ->= 9 3 4 2 5 5 ,
  9 1 6 ->= 9 3 4 2 5 1 ,
  5 3 4 ->= 1 ,
  2 3 4 ->= 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

After renaming modulo { 7->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8 }, 
it remains to prove termination of the 12-rule system
{ 0 1 2 -> 0 3 4 2 5 5 ,
  0 1 6 -> 0 3 4 2 5 1 ,
  7 1 2 -> 7 3 4 2 5 5 ,
  7 1 6 -> 7 3 4 2 5 1 ,
  5 1 2 ->= 5 3 4 2 5 5 ,
  5 1 6 ->= 5 3 4 2 5 1 ,
  2 1 2 ->= 2 3 4 2 5 5 ,
  2 1 6 ->= 2 3 4 2 5 1 ,
  8 1 2 ->= 8 3 4 2 5 5 ,
  8 1 6 ->= 8 3 4 2 5 1 ,
  5 3 4 ->= 1 ,
  2 3 4 ->= 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

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

The system is trivially terminating.