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


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


YES


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


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

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


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

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

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


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

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 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 1 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 |
 \               /
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 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 |
 \               /
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 0 |
 \               /
5 is interpreted by
 /               \
| 1 0 1 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 1 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
0 is interpreted by
 /               \
| 1 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 1 0 0 |
| 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 21-rule system
{ 1 4 -> 3 1 1 2 2 4 ,
  0 3 0 -> 2 1 1 0 2 0 ,
  4 1 4 -> 3 3 2 2 3 1 ,
  1 4 5 5 -> 0 0 1 3 4 1 ,
  4 3 0 5 -> 3 3 2 3 5 5 ,
  0 0 ->= 1 2 1 0 2 0 ,
  0 3 ->= 1 2 1 2 0 3 ,
  0 1 3 ->= 1 0 3 1 0 4 ,
  0 3 0 ->= 0 2 0 0 5 0 ,
  0 5 1 ->= 0 0 0 0 5 1 ,
  2 0 5 ->= 0 3 2 5 1 1 ,
  3 0 2 ->= 3 4 2 1 0 2 ,
  3 3 0 ->= 3 4 2 3 3 0 ,
  0 0 5 0 ->= 1 0 3 5 3 0 ,
  0 1 4 0 ->= 0 5 0 0 0 3 ,
  1 3 3 0 ->= 1 4 2 2 2 0 ,
  1 4 0 2 ->= 2 0 3 4 0 2 ,
  3 0 5 3 ->= 3 1 1 5 0 3 ,
  3 3 3 0 ->= 3 3 0 4 1 0 ,
  4 0 2 3 ->= 4 0 3 4 3 2 ,
  4 1 4 0 ->= 2 5 0 3 1 0 }


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

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

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


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

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 |
 \         /
4 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 1 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 |
 \         /
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 |
 \         /
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 |
 \         /

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


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

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

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


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

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

Remains to prove termination of the 16-rule system
{ 1 4 -> 3 1 1 2 2 4 ,
  4 1 4 -> 3 3 2 2 3 1 ,
  0 0 ->= 1 2 1 0 2 0 ,
  0 3 ->= 1 2 1 2 0 3 ,
  0 1 3 ->= 1 0 3 1 0 4 ,
  0 5 1 ->= 0 0 0 0 5 1 ,
  2 0 5 ->= 0 3 2 5 1 1 ,
  3 0 2 ->= 3 4 2 1 0 2 ,
  3 3 0 ->= 3 4 2 3 3 0 ,
  0 0 5 0 ->= 1 0 3 5 3 0 ,
  1 3 3 0 ->= 1 4 2 2 2 0 ,
  1 4 0 2 ->= 2 0 3 4 0 2 ,
  3 0 5 3 ->= 3 1 1 5 0 3 ,
  3 3 3 0 ->= 3 3 0 4 1 0 ,
  4 0 2 3 ->= 4 0 3 4 3 2 ,
  4 1 4 0 ->= 2 5 0 3 1 0 }


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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


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

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 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 |
 \             /
4 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 1 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 1 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 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 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 1 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 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
 \             /
0 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 1 |
| 0 0 0 0 0 0 0 |
 \             /

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


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

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

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


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

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

Remains to prove termination of the 9-rule system
{ 1 4 -> 3 1 1 2 2 4 ,
  0 0 ->= 1 2 1 0 2 0 ,
  0 3 ->= 1 2 1 2 0 3 ,
  0 5 1 ->= 0 0 0 0 5 1 ,
  2 0 5 ->= 0 3 2 5 1 1 ,
  3 3 0 ->= 3 4 2 3 3 0 ,
  1 3 3 0 ->= 1 4 2 2 2 0 ,
  1 4 0 2 ->= 2 0 3 4 0 2 ,
  3 3 3 0 ->= 3 3 0 4 1 0 }


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

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

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


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

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 |
 \         /
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 |
 \         /
3 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 1 1 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 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 |
 \         /
0 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 7-rule system
{ 1 4 -> 3 1 1 2 2 4 ,
  0 0 ->= 1 2 1 0 2 0 ,
  0 3 ->= 1 2 1 2 0 3 ,
  0 5 1 ->= 0 0 0 0 5 1 ,
  2 0 5 ->= 0 3 2 5 1 1 ,
  3 3 0 ->= 3 4 2 3 3 0 ,
  1 3 3 0 ->= 1 4 2 2 2 0 }


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

1 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 |
 \         /
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 |
 \         /
3 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 |
 \         /
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 |
 \         /
5 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
0 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 6-rule system
{ 1 4 -> 3 1 1 2 2 4 ,
  0 0 ->= 1 2 1 0 2 0 ,
  0 3 ->= 1 2 1 2 0 3 ,
  0 5 1 ->= 0 0 0 0 5 1 ,
  2 0 5 ->= 0 3 2 5 1 1 ,
  3 3 0 ->= 3 4 2 3 3 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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


The system is trivially terminating.