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


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YES


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

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

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


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

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

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


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

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

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


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

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

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


The system is trivially terminating.