/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES


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 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 1 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 1 1 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 0 1 1 0 0 |
| 0 0 0 0 0 0 |
| 0 1 1 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 1 0 |
| 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 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
5 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 1 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /

Remains to prove termination of the 85-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 2 3 1 0 4 ,
  0 1 4 2 -> 2 4 0 3 1 ,
  0 1 4 2 -> 3 2 1 0 4 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 2 ,
  0 1 4 2 -> 4 1 0 3 2 ,
  0 1 4 2 -> 4 1 0 4 2 ,
  0 1 4 2 -> 4 1 0 5 2 ,
  0 1 4 2 -> 2 0 3 1 0 4 ,
  0 1 4 2 -> 2 0 3 1 4 4 ,
  0 1 4 2 -> 2 3 1 4 0 4 ,
  0 1 4 2 -> 2 4 3 0 4 1 ,
  0 1 4 2 -> 2 4 3 1 0 3 ,
  0 1 4 2 -> 3 2 1 0 4 1 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 4 2 -> 3 2 3 1 0 4 ,
  0 1 4 2 -> 3 2 3 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 3 2 ,
  0 1 4 2 -> 4 0 3 1 4 2 ,
  0 1 4 2 -> 4 1 0 4 3 2 ,
  0 1 4 2 -> 4 1 0 4 5 2 ,
  0 1 4 2 -> 4 1 0 5 3 2 ,
  0 1 4 2 -> 4 1 1 0 5 2 ,
  0 1 4 2 -> 4 1 3 0 5 2 ,
  0 1 4 2 -> 4 3 0 3 1 2 ,
  0 1 4 2 -> 4 4 0 3 1 2 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 0 1 4 2 -> 0 0 3 1 2 4 ,
  0 0 1 4 2 -> 0 2 3 1 0 4 ,
  0 0 1 4 2 -> 0 2 4 0 3 1 ,
  0 0 1 4 2 -> 0 3 1 0 2 4 ,
  0 0 1 4 2 -> 1 0 3 4 0 2 ,
  0 0 1 4 2 -> 2 0 0 3 1 4 ,
  0 0 1 4 2 -> 2 1 0 4 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 3 4 2 -> 2 3 1 4 4 0 ,
  0 1 3 4 2 -> 2 4 3 0 4 1 ,
  0 1 3 4 2 -> 3 2 1 0 4 0 ,
  0 1 3 4 2 -> 4 0 3 3 1 2 ,
  0 1 3 4 2 -> 4 1 4 0 3 2 ,
  0 1 4 0 2 -> 2 0 3 1 0 4 ,
  0 1 5 0 2 -> 0 2 3 1 0 5 ,
  0 1 5 0 2 -> 3 0 5 1 0 2 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 1 5 4 2 -> 0 4 4 1 2 5 ,
  0 1 5 4 2 -> 1 0 4 5 1 2 ,
  0 1 5 4 2 -> 2 0 4 4 5 1 ,
  0 1 5 4 2 -> 4 0 2 3 1 5 ,
  0 1 5 4 2 -> 4 1 0 2 5 2 ,
  0 1 5 4 2 -> 4 1 0 5 2 5 ,
  0 1 5 4 2 -> 4 2 1 3 0 5 ,
  0 1 5 4 2 -> 4 3 1 0 2 5 ,
  0 1 5 4 2 -> 4 4 0 5 1 2 ,
  0 1 5 4 2 -> 4 4 2 1 0 5 ,
  0 1 5 4 2 -> 5 0 4 5 2 1 ,
  0 1 5 4 2 -> 5 1 2 0 4 3 ,
  0 1 5 4 2 -> 5 3 1 0 4 2 ,
  0 2 1 4 2 -> 0 4 4 1 2 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 ,
  0 2 1 4 2 -> 4 1 0 3 2 2 ,
  5 0 2 0 2 -> 5 0 3 0 2 2 ,
  5 0 2 0 2 -> 5 0 4 0 2 2 ,
  5 0 2 4 2 -> 5 4 0 3 2 2 ,
  5 1 5 0 2 -> 5 2 1 4 5 0 ,
  5 1 5 4 2 -> 5 2 1 0 4 5 ,
  5 4 2 0 2 -> 3 0 5 2 2 4 ,
  5 4 2 0 2 -> 4 0 5 3 2 2 ,
  5 4 2 0 2 -> 5 2 2 2 4 0 ,
  5 4 2 0 2 -> 5 3 2 2 4 0 ,
  5 4 2 0 2 -> 5 4 2 2 4 0 ,
  5 4 2 4 2 -> 0 4 4 5 2 2 ,
  5 4 2 4 2 -> 5 4 4 3 2 2 ,
  5 4 5 4 2 -> 4 5 0 4 5 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 10:

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

Remains to prove termination of the 82-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 2 3 1 0 4 ,
  0 1 4 2 -> 2 4 0 3 1 ,
  0 1 4 2 -> 3 2 1 0 4 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 2 ,
  0 1 4 2 -> 4 1 0 3 2 ,
  0 1 4 2 -> 4 1 0 4 2 ,
  0 1 4 2 -> 4 1 0 5 2 ,
  0 1 4 2 -> 2 0 3 1 0 4 ,
  0 1 4 2 -> 2 0 3 1 4 4 ,
  0 1 4 2 -> 2 3 1 4 0 4 ,
  0 1 4 2 -> 2 4 3 0 4 1 ,
  0 1 4 2 -> 2 4 3 1 0 3 ,
  0 1 4 2 -> 3 2 1 0 4 1 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 4 2 -> 3 2 3 1 0 4 ,
  0 1 4 2 -> 3 2 3 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 3 2 ,
  0 1 4 2 -> 4 0 3 1 4 2 ,
  0 1 4 2 -> 4 1 0 4 3 2 ,
  0 1 4 2 -> 4 1 0 4 5 2 ,
  0 1 4 2 -> 4 1 0 5 3 2 ,
  0 1 4 2 -> 4 1 1 0 5 2 ,
  0 1 4 2 -> 4 1 3 0 5 2 ,
  0 1 4 2 -> 4 3 0 3 1 2 ,
  0 1 4 2 -> 4 4 0 3 1 2 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 0 1 4 2 -> 0 0 3 1 2 4 ,
  0 0 1 4 2 -> 0 2 3 1 0 4 ,
  0 0 1 4 2 -> 0 2 4 0 3 1 ,
  0 0 1 4 2 -> 0 3 1 0 2 4 ,
  0 0 1 4 2 -> 1 0 3 4 0 2 ,
  0 0 1 4 2 -> 2 0 0 3 1 4 ,
  0 0 1 4 2 -> 2 1 0 4 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 3 4 2 -> 2 3 1 4 4 0 ,
  0 1 3 4 2 -> 2 4 3 0 4 1 ,
  0 1 3 4 2 -> 3 2 1 0 4 0 ,
  0 1 3 4 2 -> 4 0 3 3 1 2 ,
  0 1 3 4 2 -> 4 1 4 0 3 2 ,
  0 1 4 0 2 -> 2 0 3 1 0 4 ,
  0 1 5 0 2 -> 0 2 3 1 0 5 ,
  0 1 5 0 2 -> 3 0 5 1 0 2 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 1 5 4 2 -> 0 4 4 1 2 5 ,
  0 1 5 4 2 -> 1 0 4 5 1 2 ,
  0 1 5 4 2 -> 2 0 4 4 5 1 ,
  0 1 5 4 2 -> 4 0 2 3 1 5 ,
  0 1 5 4 2 -> 4 1 0 2 5 2 ,
  0 1 5 4 2 -> 4 1 0 5 2 5 ,
  0 1 5 4 2 -> 4 2 1 3 0 5 ,
  0 1 5 4 2 -> 4 3 1 0 2 5 ,
  0 1 5 4 2 -> 4 4 0 5 1 2 ,
  0 1 5 4 2 -> 4 4 2 1 0 5 ,
  0 1 5 4 2 -> 5 0 4 5 2 1 ,
  0 1 5 4 2 -> 5 1 2 0 4 3 ,
  0 1 5 4 2 -> 5 3 1 0 4 2 ,
  0 2 1 4 2 -> 0 4 4 1 2 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 ,
  0 2 1 4 2 -> 4 1 0 3 2 2 ,
  5 0 2 0 2 -> 5 0 3 0 2 2 ,
  5 0 2 0 2 -> 5 0 4 0 2 2 ,
  5 1 5 0 2 -> 5 2 1 4 5 0 ,
  5 1 5 4 2 -> 5 2 1 0 4 5 ,
  5 4 2 0 2 -> 3 0 5 2 2 4 ,
  5 4 2 0 2 -> 4 0 5 3 2 2 ,
  5 4 2 0 2 -> 5 2 2 2 4 0 ,
  5 4 2 0 2 -> 5 3 2 2 4 0 ,
  5 4 2 0 2 -> 5 4 2 2 4 0 ,
  5 4 5 4 2 -> 4 5 0 4 5 2 }


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

Remains to prove termination of the 81-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 2 3 1 0 4 ,
  0 1 4 2 -> 2 4 0 3 1 ,
  0 1 4 2 -> 3 2 1 0 4 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 2 ,
  0 1 4 2 -> 4 1 0 3 2 ,
  0 1 4 2 -> 4 1 0 4 2 ,
  0 1 4 2 -> 4 1 0 5 2 ,
  0 1 4 2 -> 2 0 3 1 0 4 ,
  0 1 4 2 -> 2 0 3 1 4 4 ,
  0 1 4 2 -> 2 3 1 4 0 4 ,
  0 1 4 2 -> 2 4 3 0 4 1 ,
  0 1 4 2 -> 2 4 3 1 0 3 ,
  0 1 4 2 -> 3 2 1 0 4 1 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 4 2 -> 3 2 3 1 0 4 ,
  0 1 4 2 -> 3 2 3 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 3 2 ,
  0 1 4 2 -> 4 0 3 1 4 2 ,
  0 1 4 2 -> 4 1 0 4 3 2 ,
  0 1 4 2 -> 4 1 0 4 5 2 ,
  0 1 4 2 -> 4 1 0 5 3 2 ,
  0 1 4 2 -> 4 1 1 0 5 2 ,
  0 1 4 2 -> 4 1 3 0 5 2 ,
  0 1 4 2 -> 4 3 0 3 1 2 ,
  0 1 4 2 -> 4 4 0 3 1 2 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 0 1 4 2 -> 0 0 3 1 2 4 ,
  0 0 1 4 2 -> 0 2 3 1 0 4 ,
  0 0 1 4 2 -> 0 2 4 0 3 1 ,
  0 0 1 4 2 -> 0 3 1 0 2 4 ,
  0 0 1 4 2 -> 1 0 3 4 0 2 ,
  0 0 1 4 2 -> 2 0 0 3 1 4 ,
  0 0 1 4 2 -> 2 1 0 4 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 3 4 2 -> 2 3 1 4 4 0 ,
  0 1 3 4 2 -> 2 4 3 0 4 1 ,
  0 1 3 4 2 -> 3 2 1 0 4 0 ,
  0 1 3 4 2 -> 4 0 3 3 1 2 ,
  0 1 3 4 2 -> 4 1 4 0 3 2 ,
  0 1 4 0 2 -> 2 0 3 1 0 4 ,
  0 1 5 0 2 -> 0 2 3 1 0 5 ,
  0 1 5 0 2 -> 3 0 5 1 0 2 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 1 5 4 2 -> 0 4 4 1 2 5 ,
  0 1 5 4 2 -> 1 0 4 5 1 2 ,
  0 1 5 4 2 -> 2 0 4 4 5 1 ,
  0 1 5 4 2 -> 4 0 2 3 1 5 ,
  0 1 5 4 2 -> 4 1 0 2 5 2 ,
  0 1 5 4 2 -> 4 1 0 5 2 5 ,
  0 1 5 4 2 -> 4 2 1 3 0 5 ,
  0 1 5 4 2 -> 4 3 1 0 2 5 ,
  0 1 5 4 2 -> 4 4 0 5 1 2 ,
  0 1 5 4 2 -> 4 4 2 1 0 5 ,
  0 1 5 4 2 -> 5 0 4 5 2 1 ,
  0 1 5 4 2 -> 5 1 2 0 4 3 ,
  0 1 5 4 2 -> 5 3 1 0 4 2 ,
  0 2 1 4 2 -> 0 4 4 1 2 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 ,
  0 2 1 4 2 -> 4 1 0 3 2 2 ,
  5 0 2 0 2 -> 5 0 3 0 2 2 ,
  5 0 2 0 2 -> 5 0 4 0 2 2 ,
  5 1 5 0 2 -> 5 2 1 4 5 0 ,
  5 1 5 4 2 -> 5 2 1 0 4 5 ,
  5 4 2 0 2 -> 3 0 5 2 2 4 ,
  5 4 2 0 2 -> 4 0 5 3 2 2 ,
  5 4 2 0 2 -> 5 2 2 2 4 0 ,
  5 4 2 0 2 -> 5 3 2 2 4 0 ,
  5 4 2 0 2 -> 5 4 2 2 4 0 }


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 1 0 0 2 |
| 0 1 1 0 1 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 2 0 0 1 0 |
 \           /
2 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 1 0 1 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 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 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 |
 \           /
5 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 1 0 |
| 0 1 0 0 1 0 |
| 0 0 0 0 0 0 |
 \           /

Remains to prove termination of the 59-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 2 3 1 0 4 ,
  0 1 4 2 -> 2 4 0 3 1 ,
  0 1 4 2 -> 3 2 1 0 4 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 2 ,
  0 1 4 2 -> 4 1 0 3 2 ,
  0 1 4 2 -> 4 1 0 4 2 ,
  0 1 4 2 -> 4 1 0 5 2 ,
  0 1 4 2 -> 2 0 3 1 0 4 ,
  0 1 4 2 -> 2 0 3 1 4 4 ,
  0 1 4 2 -> 2 3 1 4 0 4 ,
  0 1 4 2 -> 2 4 3 0 4 1 ,
  0 1 4 2 -> 2 4 3 1 0 3 ,
  0 1 4 2 -> 3 2 1 0 4 1 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 4 2 -> 3 2 3 1 0 4 ,
  0 1 4 2 -> 3 2 3 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 3 2 ,
  0 1 4 2 -> 4 0 3 1 4 2 ,
  0 1 4 2 -> 4 1 0 4 3 2 ,
  0 1 4 2 -> 4 1 0 4 5 2 ,
  0 1 4 2 -> 4 1 0 5 3 2 ,
  0 1 4 2 -> 4 1 1 0 5 2 ,
  0 1 4 2 -> 4 1 3 0 5 2 ,
  0 1 4 2 -> 4 3 0 3 1 2 ,
  0 1 4 2 -> 4 4 0 3 1 2 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 0 1 4 2 -> 0 0 3 1 2 4 ,
  0 0 1 4 2 -> 0 2 3 1 0 4 ,
  0 0 1 4 2 -> 0 2 4 0 3 1 ,
  0 0 1 4 2 -> 0 3 1 0 2 4 ,
  0 0 1 4 2 -> 1 0 3 4 0 2 ,
  0 0 1 4 2 -> 2 0 0 3 1 4 ,
  0 0 1 4 2 -> 2 1 0 4 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 4 0 2 -> 2 0 3 1 0 4 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 2 1 4 2 -> 0 4 4 1 2 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 ,
  0 2 1 4 2 -> 4 1 0 3 2 2 ,
  5 0 2 0 2 -> 5 0 3 0 2 2 ,
  5 0 2 0 2 -> 5 0 4 0 2 2 ,
  5 4 2 0 2 -> 3 0 5 2 2 4 ,
  5 4 2 0 2 -> 4 0 5 3 2 2 ,
  5 4 2 0 2 -> 5 2 2 2 4 0 ,
  5 4 2 0 2 -> 5 3 2 2 4 0 ,
  5 4 2 0 2 -> 5 4 2 2 4 0 }


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 1 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
 \           /
1 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 |
 \           /
2 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 1 0 |
| 0 0 0 0 0 0 |
| 0 1 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 0 |
| 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 0 0 0 |
 \           /
5 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 |
 \           /

Remains to prove termination of the 57-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 2 3 1 0 4 ,
  0 1 4 2 -> 2 4 0 3 1 ,
  0 1 4 2 -> 3 2 1 0 4 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 2 ,
  0 1 4 2 -> 4 1 0 3 2 ,
  0 1 4 2 -> 4 1 0 4 2 ,
  0 1 4 2 -> 4 1 0 5 2 ,
  0 1 4 2 -> 2 0 3 1 0 4 ,
  0 1 4 2 -> 2 0 3 1 4 4 ,
  0 1 4 2 -> 2 3 1 4 0 4 ,
  0 1 4 2 -> 2 4 3 0 4 1 ,
  0 1 4 2 -> 2 4 3 1 0 3 ,
  0 1 4 2 -> 3 2 1 0 4 1 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 4 2 -> 3 2 3 1 0 4 ,
  0 1 4 2 -> 3 2 3 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 3 2 ,
  0 1 4 2 -> 4 0 3 1 4 2 ,
  0 1 4 2 -> 4 1 0 4 3 2 ,
  0 1 4 2 -> 4 1 0 4 5 2 ,
  0 1 4 2 -> 4 1 0 5 3 2 ,
  0 1 4 2 -> 4 1 1 0 5 2 ,
  0 1 4 2 -> 4 1 3 0 5 2 ,
  0 1 4 2 -> 4 3 0 3 1 2 ,
  0 1 4 2 -> 4 4 0 3 1 2 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 0 1 4 2 -> 0 0 3 1 2 4 ,
  0 0 1 4 2 -> 0 2 3 1 0 4 ,
  0 0 1 4 2 -> 0 2 4 0 3 1 ,
  0 0 1 4 2 -> 0 3 1 0 2 4 ,
  0 0 1 4 2 -> 1 0 3 4 0 2 ,
  0 0 1 4 2 -> 2 0 0 3 1 4 ,
  0 0 1 4 2 -> 2 1 0 4 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 4 0 2 -> 2 0 3 1 0 4 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 2 1 4 2 -> 0 4 4 1 2 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 ,
  0 2 1 4 2 -> 4 1 0 3 2 2 ,
  5 4 2 0 2 -> 3 0 5 2 2 4 ,
  5 4 2 0 2 -> 4 0 5 3 2 2 ,
  5 4 2 0 2 -> 5 2 2 2 4 0 ,
  5 4 2 0 2 -> 5 3 2 2 4 0 ,
  5 4 2 0 2 -> 5 4 2 2 4 0 }


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 1 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
 \           /
1 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 1 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 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 1 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 0 |
| 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 1 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 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 |
 \           /

Remains to prove termination of the 52-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 2 3 1 0 4 ,
  0 1 4 2 -> 2 4 0 3 1 ,
  0 1 4 2 -> 3 2 1 0 4 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 2 ,
  0 1 4 2 -> 4 1 0 3 2 ,
  0 1 4 2 -> 4 1 0 4 2 ,
  0 1 4 2 -> 4 1 0 5 2 ,
  0 1 4 2 -> 2 0 3 1 0 4 ,
  0 1 4 2 -> 2 0 3 1 4 4 ,
  0 1 4 2 -> 2 3 1 4 0 4 ,
  0 1 4 2 -> 2 4 3 0 4 1 ,
  0 1 4 2 -> 2 4 3 1 0 3 ,
  0 1 4 2 -> 3 2 1 0 4 1 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 4 2 -> 3 2 3 1 0 4 ,
  0 1 4 2 -> 3 2 3 1 4 0 ,
  0 1 4 2 -> 4 0 3 1 3 2 ,
  0 1 4 2 -> 4 0 3 1 4 2 ,
  0 1 4 2 -> 4 1 0 4 3 2 ,
  0 1 4 2 -> 4 1 0 4 5 2 ,
  0 1 4 2 -> 4 1 0 5 3 2 ,
  0 1 4 2 -> 4 1 1 0 5 2 ,
  0 1 4 2 -> 4 1 3 0 5 2 ,
  0 1 4 2 -> 4 3 0 3 1 2 ,
  0 1 4 2 -> 4 4 0 3 1 2 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 0 1 4 2 -> 0 0 3 1 2 4 ,
  0 0 1 4 2 -> 0 2 3 1 0 4 ,
  0 0 1 4 2 -> 0 2 4 0 3 1 ,
  0 0 1 4 2 -> 0 3 1 0 2 4 ,
  0 0 1 4 2 -> 1 0 3 4 0 2 ,
  0 0 1 4 2 -> 2 0 0 3 1 4 ,
  0 0 1 4 2 -> 2 1 0 4 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 4 0 2 -> 2 0 3 1 0 4 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 2 1 4 2 -> 0 4 4 1 2 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 ,
  0 2 1 4 2 -> 4 1 0 3 2 2 }


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

Remains to prove termination of the 18-rule system
{ 0 1 0 2 -> 2 0 3 1 0 ,
  0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 0 3 1 0 4 ,
  0 1 0 2 -> 2 2 0 3 1 0 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 0 2 -> 2 3 1 0 3 0 ,
  0 1 0 2 -> 4 1 0 3 0 2 ,
  0 1 0 2 -> 4 1 0 4 0 2 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 0 1 0 2 -> 1 0 4 0 0 2 ,
  0 0 1 0 2 -> 2 1 0 3 0 0 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 }


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

Remains to prove termination of the 10-rule system
{ 0 1 0 2 -> 2 0 0 3 1 2 ,
  0 1 0 2 -> 2 3 1 0 0 2 ,
  0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 0 1 0 2 -> 1 0 0 2 0 4 ,
  0 1 2 0 2 -> 2 0 1 0 4 2 ,
  0 1 2 4 2 -> 2 3 1 0 2 4 ,
  0 1 2 4 2 -> 4 1 0 2 2 4 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 }


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

Remains to prove termination of the 4-rule system
{ 0 1 4 2 -> 3 2 1 4 0 ,
  0 1 4 2 -> 3 2 2 1 4 0 ,
  0 1 5 0 2 -> 5 1 3 0 0 2 ,
  0 2 1 4 2 -> 3 2 2 1 4 0 }


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

Remains to prove termination of the 1-rule system
{ 0 1 5 0 2 -> 5 1 3 0 0 2 }


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 1 |
| 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 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 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 0 |
| 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 0 0 0 |
 \           /
5 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 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

Remains to prove termination of the 0-rule system
{ }


The system is trivially terminating.