/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 10:

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

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


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

0 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 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 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 1 1 1 0 0 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 1 0 0 0 0 0 0 0 0 |
 \                   /
2 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 1 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 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 |
 \                   /
3 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 1 0 0 0 0 0 0 0 |
| 0 0 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 1 0 0 0 |
 \                   /
4 is interpreted by
 /                   \
| 1 0 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 1 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
 \                   /
5 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 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 1 0 0 |
| 0 0 0 0 0 0 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 48-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 1 1 -> 0 1 1 1 3 2 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 1 -> 0 1 1 3 5 ,
  0 5 1 1 -> 0 1 3 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 1 -> 0 3 1 5 4 ,
  0 5 4 1 -> 0 0 4 1 1 5 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  2 0 2 4 -> 2 2 4 0 0 ,
  2 0 5 1 -> 0 0 0 5 2 1 ,
  2 0 5 1 -> 5 0 3 5 2 1 ,
  2 0 5 1 -> 5 3 0 5 2 1 ,
  2 0 5 4 -> 2 4 0 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 0 2 1 1 -> 0 3 0 1 2 1 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 0 2 4 -> 0 0 2 1 2 4 ,
  0 2 0 5 1 -> 5 0 0 0 2 1 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 0 5 1 1 -> 5 0 2 3 1 1 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 1 2 1 1 -> 3 4 1 1 2 1 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

0 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 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 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 1 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 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 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
 \                   /
2 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 1 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 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 |
 \                   /
3 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 1 0 0 0 0 0 0 0 |
| 0 0 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 1 0 0 0 |
 \                   /
4 is interpreted by
 /                   \
| 1 0 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
 \                   /
5 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 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 1 0 0 |
| 0 0 0 0 0 0 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 47-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 1 1 -> 0 1 1 1 3 2 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 1 -> 0 1 1 3 5 ,
  0 5 1 1 -> 0 1 3 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 1 -> 0 3 1 5 4 ,
  0 5 4 1 -> 0 0 4 1 1 5 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  2 0 2 4 -> 2 2 4 0 0 ,
  2 0 5 1 -> 0 0 0 5 2 1 ,
  2 0 5 1 -> 5 0 3 5 2 1 ,
  2 0 5 1 -> 5 3 0 5 2 1 ,
  2 0 5 4 -> 2 4 0 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 0 2 1 1 -> 0 3 0 1 2 1 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 0 2 4 -> 0 0 2 1 2 4 ,
  0 2 0 5 1 -> 5 0 0 0 2 1 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 0 5 1 1 -> 5 0 2 3 1 1 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

0 is interpreted by
 /                 \
| 1 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 1 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 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 1 0 0 0 0 0 0 0 |
| 0 0 0 0 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 |
 \                 /
2 is interpreted by
 /                 \
| 1 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 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 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 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 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 1 0 0 0 |
 \                 /
4 is interpreted by
 /                 \
| 1 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 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
 \                 /
5 is interpreted by
 /                 \
| 1 0 0 0 0 0 0 0 0 |
| 0 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 1 0 0 |
| 0 0 0 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 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 1 1 -> 0 1 1 1 3 2 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 1 -> 0 1 1 3 5 ,
  0 5 1 1 -> 0 1 3 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  2 0 2 4 -> 2 2 4 0 0 ,
  2 0 5 1 -> 0 0 0 5 2 1 ,
  2 0 5 1 -> 5 0 3 5 2 1 ,
  2 0 5 1 -> 5 3 0 5 2 1 ,
  2 0 5 4 -> 2 4 0 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 0 2 1 1 -> 0 3 0 1 2 1 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 0 2 4 -> 0 0 2 1 2 4 ,
  0 2 0 5 1 -> 5 0 0 0 2 1 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 0 5 1 1 -> 5 0 2 3 1 1 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

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

Remains to prove termination of the 40-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  2 0 2 4 -> 2 2 4 0 0 ,
  2 0 5 1 -> 0 0 0 5 2 1 ,
  2 0 5 1 -> 5 0 3 5 2 1 ,
  2 0 5 1 -> 5 3 0 5 2 1 ,
  2 0 5 4 -> 2 4 0 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 0 2 4 -> 0 0 2 1 2 4 ,
  0 2 0 5 1 -> 5 0 0 0 2 1 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

0 is interpreted by
 /                 \
| 1 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 0 0 0 0 0 0 0 0 |
| 0 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 is interpreted by
 /                 \
| 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 0 0 0 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 |
 \                 /
2 is interpreted by
 /                 \
| 1 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 1 |
| 0 0 0 0 0 0 0 0 0 |
 \                 /
3 is interpreted by
 /                 \
| 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 1 0 0 0 |
| 0 0 0 0 0 0 0 0 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 |
 \                 /
4 is interpreted by
 /                 \
| 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 |
 \                 /
5 is interpreted by
 /                 \
| 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 1 0 0 |
| 0 0 0 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 36-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  2 0 2 4 -> 2 2 4 0 0 ,
  2 0 5 4 -> 2 4 0 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 0 2 4 -> 0 0 2 1 2 4 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 1 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 0 0 0 1 |
 \         /
2 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 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 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 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 35-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  2 0 2 4 -> 2 2 4 0 0 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 0 2 4 -> 0 0 2 1 2 4 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 1 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 0 0 0 1 |
 \         /
2 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 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 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 33-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 4 5 1 -> 0 0 0 4 1 5 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 1 5 4 1 -> 4 0 1 1 3 5 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 1 5 1 -> 0 5 2 1 1 0 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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


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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

Remains to prove termination of the 30-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 2 3 5 1 -> 5 2 1 0 0 3 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

Remains to prove termination of the 29-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 0 1 2 4 -> 2 2 1 3 4 0 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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

Remains to prove termination of the 28-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  0 5 4 4 -> 4 0 4 3 5 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 3 2 4 -> 2 3 4 3 5 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  0 5 5 4 2 -> 4 0 3 5 5 2 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

Remains to prove termination of the 25-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 2 4 4 -> 3 0 4 2 4 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 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 1 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 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 1 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 24-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 1 4 -> 0 3 3 4 1 5 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 1 5 1 4 -> 0 4 3 1 1 5 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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


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

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 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 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 0 |
| 0 1 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 22-rule system
{ 0 1 0 2 -> 0 0 1 3 2 ,
  0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 0 2 4 -> 0 4 0 5 2 4 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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


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

Remains to prove termination of the 20-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  0 2 3 2 -> 0 3 0 3 2 2 ,
  0 4 0 2 -> 3 0 0 4 2 ,
  0 4 0 2 -> 3 0 0 0 4 2 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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


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

Remains to prove termination of the 17-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  0 5 3 2 -> 0 3 0 5 5 2 ,
  0 5 3 2 -> 3 0 3 5 5 2 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 15-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 2 1 3 2 -> 3 0 3 1 2 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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

Remains to prove termination of the 14-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 4 0 4 2 -> 3 0 0 4 4 2 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

Remains to prove termination of the 13-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 5 1 3 2 -> 0 3 4 1 5 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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

Remains to prove termination of the 12-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  0 5 4 3 2 -> 0 0 3 4 2 5 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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

Remains to prove termination of the 11-rule system
{ 0 1 2 2 -> 0 3 2 2 1 ,
  5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  2 5 5 1 1 -> 5 5 2 1 1 3 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 1 5 1 -> 5 0 3 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

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

Remains to prove termination of the 8-rule system
{ 5 1 0 2 -> 2 5 0 3 1 ,
  5 4 0 2 -> 5 0 3 0 4 2 ,
  3 5 0 2 1 -> 1 2 5 0 3 3 ,
  4 3 5 1 1 -> 3 4 1 1 1 5 ,
  5 0 5 0 2 -> 2 0 0 0 5 5 ,
  5 1 4 5 1 -> 5 0 1 1 5 4 ,
  5 1 4 5 1 -> 5 3 4 1 1 5 ,
  5 3 1 5 4 -> 5 3 4 1 3 5 }


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

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


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

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


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


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

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


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

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


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

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


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

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

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


The system is trivially terminating.