/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

After renaming modulo { a->0, b->1, c->2, d->3 }, 
it remains to prove termination of the 8-rule system
{ 0 0 -> 0 1 0 1 0 ,
  2 0 -> 0 1 0 0 2 ,
  1 1 1 -> 0 1 ,
  2 1 -> 0 0 2 ,
  2 1 -> 1 0 3 ,
  3 3 -> 3 1 3 1 3 ,
  2 2 -> 2 3 2 ,
  0 0 0 -> 0 1 1 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, 
it remains to prove termination of the 7-rule system
{ 0 0 -> 0 1 0 1 0 ,
  2 0 -> 0 1 0 0 2 ,
  1 1 1 -> 0 1 ,
  2 1 -> 0 0 2 ,
  3 3 -> 3 1 3 1 3 ,
  2 2 -> 2 3 2 ,
  0 0 0 -> 0 1 1 }


Applying sparse untiling TRFCU(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo { 0->0, 1->1 },
it remains to prove termination of the 3-rule system
{ 0 0 -> 0 1 0 1 0 ,
  1 1 1 -> 0 1 ,
  0 0 0 -> 0 1 1 }


Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo { (0,0)->0, (0,1)->1, (1,0)->2, (0,3)->3, (2,0)->4, (1,1)->5, (1,3)->6 },
it remains to prove termination of the 24-rule system
{ 0 0 0 -> 0 1 2 1 2 0 ,
  0 0 1 -> 0 1 2 1 2 1 ,
  0 0 3 -> 0 1 2 1 2 3 ,
  2 0 0 -> 2 1 2 1 2 0 ,
  2 0 1 -> 2 1 2 1 2 1 ,
  2 0 3 -> 2 1 2 1 2 3 ,
  4 0 0 -> 4 1 2 1 2 0 ,
  4 0 1 -> 4 1 2 1 2 1 ,
  4 0 3 -> 4 1 2 1 2 3 ,
  1 5 5 2 -> 0 1 2 ,
  1 5 5 5 -> 0 1 5 ,
  1 5 5 6 -> 0 1 6 ,
  5 5 5 2 -> 2 1 2 ,
  5 5 5 5 -> 2 1 5 ,
  5 5 5 6 -> 2 1 6 ,
  0 0 0 0 -> 0 1 5 2 ,
  0 0 0 1 -> 0 1 5 5 ,
  0 0 0 3 -> 0 1 5 6 ,
  2 0 0 0 -> 2 1 5 2 ,
  2 0 0 1 -> 2 1 5 5 ,
  2 0 0 3 -> 2 1 5 6 ,
  4 0 0 0 -> 4 1 5 2 ,
  4 0 0 1 -> 4 1 5 5 ,
  4 0 0 3 -> 4 1 5 6 }


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

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

After renaming modulo { 0->0, 1->1, 5->2, 2->3, 4->4 }, 
it remains to prove termination of the 3-rule system
{ 0 0 0 1 -> 0 1 2 2 ,
  3 0 0 1 -> 3 1 2 2 ,
  4 0 0 1 -> 4 1 2 2 }


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

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

After renaming modulo {  }, 
it remains to prove termination of the 0-rule system
{ }

The system is trivially terminating.