/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:

3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 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 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 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 11-rule system
{ 3 1 -> 4 1 ,
  3 5 -> 8 9 7 ,
  9 -> 3 2 3 ,
  8 4 -> 6 ,
  2 6 -> 4 3 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  8 8 4 -> 1 9 ,
  7 1 -> 6 9 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 1 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 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
9 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
6 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 |
 \         /
8 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 |
 \         /
7 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 0 0 0 0 |
 \         /

Remains to prove termination of the 10-rule system
{ 3 1 -> 4 1 ,
  3 5 -> 8 9 7 ,
  9 -> 3 2 3 ,
  8 4 -> 6 ,
  2 6 -> 4 3 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  7 1 -> 6 9 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 9-rule system
{ 3 1 -> 4 1 ,
  3 5 -> 8 9 7 ,
  8 4 -> 6 ,
  2 6 -> 4 3 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  7 1 -> 6 9 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 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 8-rule system
{ 3 1 -> 4 1 ,
  3 5 -> 8 9 7 ,
  2 6 -> 4 3 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  7 1 -> 6 9 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ 3 5 -> 8 9 7 ,
  2 6 -> 4 3 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  7 1 -> 6 9 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
4 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 |
 \     /
9 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 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 6-rule system
{ 3 5 -> 8 9 7 ,
  2 6 -> 4 3 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ 3 5 -> 8 9 7 ,
  3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ 3 8 -> 3 2 7 ,
  9 -> 5 0 2 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ 3 8 -> 3 2 7 ,
  3 9 -> 9 3 ,
  7 5 -> 1 0 }


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

3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 2-rule system
{ 3 8 -> 3 2 7 ,
  3 9 -> 9 3 }


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

3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 1-rule system
{ 3 9 -> 9 3 }


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

3 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 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 0-rule system
{ }


The system is trivially terminating.