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


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YES


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

Remains to prove termination of the 59-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  0 1 5 5 1 -> 1 2 2 4 4 2 0 3 2 5 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  5 0 1 1 5 -> 5 5 2 0 3 1 4 4 1 3 ,
  0 0 1 5 4 1 -> 0 3 1 4 3 3 3 0 0 1 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  0 5 0 1 4 5 -> 3 4 5 0 3 1 3 5 4 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 1 2 1 5 -> 4 0 0 5 3 1 4 1 4 5 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  0 1 0 0 5 0 5 -> 4 1 4 2 4 2 4 2 1 2 ,
  0 1 0 2 5 0 5 -> 0 0 4 3 2 5 3 5 4 4 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 1 0 1 1 2 4 -> 3 5 2 5 0 0 3 4 4 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 1 5 1 3 -> 3 0 4 2 1 0 3 3 5 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  4 1 4 0 4 1 1 -> 0 0 3 0 2 1 4 5 2 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 1 5 0 5 1 5 -> 0 3 5 2 4 0 4 1 3 4 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 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 0 0 0 1 |
| 0 0 0 0 0 1 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 1 0 1 0 |
| 0 0 0 0 1 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 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 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 1 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 1 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 1 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 1 |
 \           /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

Remains to prove termination of the 54-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  0 5 0 1 4 5 -> 3 4 5 0 3 1 3 5 4 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 1 2 1 5 -> 4 0 0 5 3 1 4 1 4 5 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  0 1 0 0 5 0 5 -> 4 1 4 2 4 2 4 2 1 2 ,
  0 1 0 2 5 0 5 -> 0 0 4 3 2 5 3 5 4 4 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  4 1 4 0 4 1 1 -> 0 0 3 0 2 1 4 5 2 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 1 5 0 5 1 5 -> 0 3 5 2 4 0 4 1 3 4 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 53-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  0 5 0 1 4 5 -> 3 4 5 0 3 1 3 5 4 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 1 2 1 5 -> 4 0 0 5 3 1 4 1 4 5 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  0 1 0 0 5 0 5 -> 4 1 4 2 4 2 4 2 1 2 ,
  0 1 0 2 5 0 5 -> 0 0 4 3 2 5 3 5 4 4 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 1 5 0 5 1 5 -> 0 3 5 2 4 0 4 1 3 4 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 51-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  0 5 0 1 4 5 -> 3 4 5 0 3 1 3 5 4 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  0 1 0 0 5 0 5 -> 4 1 4 2 4 2 4 2 1 2 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 1 5 0 5 1 5 -> 0 3 5 2 4 0 4 1 3 4 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 50-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  0 5 0 1 4 5 -> 3 4 5 0 3 1 3 5 4 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  0 1 0 0 5 0 5 -> 4 1 4 2 4 2 4 2 1 2 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 49-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  0 5 0 1 4 5 -> 3 4 5 0 3 1 3 5 4 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

Remains to prove termination of the 48-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 0 5 0 5 -> 4 4 4 5 5 4 3 0 5 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 47-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 1 1 -> 2 2 0 3 3 4 3 0 4 1 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 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 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
 \           /
1 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 1 0 1 |
| 0 1 0 0 0 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 0 0 0 0 1 |
 \           /
3 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 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 1 0 0 0 |
| 0 0 0 1 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 1 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /

Remains to prove termination of the 46-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  0 1 2 4 1 5 -> 4 3 5 2 3 2 5 5 1 3 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


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

Remains to prove termination of the 45-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 4 2 5 0 4 5 -> 5 2 3 5 3 0 4 2 3 1 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 44-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 3 2 ->= 3 3 0 0 3 5 4 1 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 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 1 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 1 0 0 |
| 0 1 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 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 1 |
| 0 0 0 0 1 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 1 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 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
 \         /

Remains to prove termination of the 43-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 0 5 0 5 0 5 -> 1 2 2 3 0 3 3 3 1 2 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 42-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 0 5 5 -> 4 0 4 0 3 4 1 5 4 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 4 0 5 1 0 4 -> 1 4 3 5 4 5 1 3 3 0 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 1 2 0 0 5 5 -> 4 3 0 1 2 2 3 1 2 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

Remains to prove termination of the 39-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  1 2 5 1 5 -> 2 3 5 0 2 2 3 4 4 4 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 12:

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

Remains to prove termination of the 38-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  3 5 1 1 0 1 5 -> 0 3 4 1 4 0 2 5 3 1 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 19:

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

Remains to prove termination of the 37-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  4 0 1 3 0 -> 4 2 4 0 2 3 4 2 3 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 12:

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

Remains to prove termination of the 36-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 0 1 5 1 1 0 -> 5 2 2 1 2 4 4 3 1 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 35-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 0 0 1 3 5 0 -> 1 3 4 0 3 1 2 3 1 0 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 34-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 0 2 4 1 -> 3 0 4 5 1 0 3 4 2 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 33-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  1 2 0 2 4 1 -> 1 4 3 1 2 3 4 4 2 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 12:

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

Remains to prove termination of the 32-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 3 1 3 2 ->= 3 3 3 0 3 4 1 4 3 2 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 11:

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

Remains to prove termination of the 31-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 3 3 -> 4 5 0 2 2 2 0 2 3 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  0 1 1 1 0 4 -> 2 1 5 4 3 0 3 5 5 5 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  0 0 0 5 1 4 4 -> 4 2 3 0 4 4 1 1 3 0 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 11:

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

Remains to prove termination of the 28-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  5 4 1 3 3 ->= 5 3 4 4 3 5 2 2 3 3 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 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 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 0 0 0 |
| 0 0 0 0 1 0 |
| 0 1 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 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 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 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 |
 \           /
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 27-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  3 2 1 5 1 3 -> 0 2 4 4 0 0 4 3 0 3 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


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

Remains to prove termination of the 26-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 0 5 3 ->= 4 2 0 2 0 3 4 2 5 3 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 0 0 1 5 2 2 ->= 4 2 0 0 4 5 1 3 2 2 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 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 1 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 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 1 0 0 0 |
| 0 0 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 1 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 1 |
| 0 0 0 0 0 |
 \         /

Remains to prove termination of the 24-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 0 1 0 0 -> 2 3 2 3 2 5 1 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 23-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  5 3 2 ->= 0 3 0 2 2 0 3 2 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 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 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 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 1 0 0 0 1 |
| 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 1 0 0 0 0 |
 \           /
3 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 |
 \           /
4 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 |
 \           /
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 22-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 1 4 0 2 0 0 ->= 4 3 0 3 5 0 1 0 0 0 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

Remains to prove termination of the 21-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 0 1 3 2 4 3 -> 4 0 0 4 4 3 5 0 5 2 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

0 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 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 |
 \               /
1 is interpreted by
 /               \
| 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 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 0 0 0 0 0 0 |
 \               /
2 is interpreted by
 /               \
| 1 0 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 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 |
 \               /
3 is interpreted by
 /               \
| 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 1 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 1 1 0 0 0 0 0 |
 \               /
4 is interpreted by
 /               \
| 1 0 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 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 |
 \               /
5 is interpreted by
 /               \
| 1 0 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 0 0 |
| 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 20-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 2 0 5 0 1 3 -> 5 5 1 3 1 2 1 4 2 3 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 12:

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

Remains to prove termination of the 19-rule system
{ 0 1 2 -> 2 3 3 3 0 2 2 4 4 2 ,
  2 5 0 -> 4 2 2 3 4 3 0 2 3 0 ,
  0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  0 1 2 4 5 -> 4 2 2 0 3 1 3 3 4 2 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  5 0 0 5 2 -> 0 5 2 0 3 0 4 0 2 3 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  2 5 2 5 0 4 -> 5 3 5 3 0 4 2 4 0 4 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  1 5 0 0 1 4 4 -> 4 5 4 4 3 3 4 3 4 5 ,
  2 2 5 5 0 0 5 -> 5 3 4 3 1 2 0 3 0 1 ,
  2 5 0 5 2 4 4 -> 4 4 0 4 2 3 1 0 0 3 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  2 5 4 2 1 0 2 -> 2 4 0 3 3 5 1 4 0 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 ,
  0 0 5 2 2 4 ->= 0 4 4 3 0 2 3 5 3 4 ,
  0 1 5 2 0 2 4 ->= 2 2 3 3 4 4 0 5 2 4 ,
  1 0 5 4 0 5 0 ->= 5 4 1 5 0 2 4 4 1 0 }


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

Remains to prove termination of the 7-rule system
{ 0 1 0 3 -> 5 2 2 2 0 0 3 2 0 3 ,
  2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  1 3 2 0 1 2 2 -> 3 3 4 4 0 1 2 3 2 2 ,
  2 5 1 1 2 4 2 -> 0 3 1 2 0 3 2 4 2 2 ,
  5 1 1 0 0 1 4 -> 5 1 1 4 2 2 4 4 2 2 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 }


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

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


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 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 0 0 0 |
| 0 1 0 0 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 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 3-rule system
{ 2 0 5 4 0 -> 2 0 0 0 0 4 0 4 5 0 ,
  2 2 5 0 0 5 -> 2 3 0 5 2 2 2 3 4 1 ,
  0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 }


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 1 |
| 0 1 |
 \   /

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


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 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 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 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 |
 \           /
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 1 |
| 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 1-rule system
{ 0 5 5 4 ->= 4 0 0 4 3 4 5 3 5 4 }


The system is trivially terminating.