/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

After renaming modulo { 4->0, 2->1, 0->2, 5->3, 3->4, 1->5 }, 
it remains to prove termination of the 10-rule system
{ 0 1 0 -> 1 2 2 3 4 4 3 1 2 0 ,
  0 0 1 0 1 -> 1 2 3 1 5 0 2 1 2 5 ,
  2 3 0 1 0 4 -> 3 5 3 3 4 3 4 2 2 2 ,
  5 5 0 3 4 4 -> 5 4 5 5 4 2 5 1 1 5 ,
  4 5 0 4 5 1 -> 2 2 5 5 0 1 4 2 2 4 ,
  4 1 0 1 0 5 -> 2 1 5 5 5 3 4 5 4 4 ,
  4 4 2 0 5 1 -> 4 3 5 1 2 1 2 3 4 5 ,
  0 5 0 3 2 3 0 -> 0 5 3 4 5 2 3 4 5 2 ,
  0 0 2 3 0 1 1 -> 0 2 0 4 0 0 0 3 0 5 ,
  3 0 3 4 1 0 4 -> 1 3 3 3 2 0 3 2 5 0 }


The system was reversed.

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 10-rule system
{ 0 1 0 -> 0 2 1 3 4 4 3 2 2 1 ,
  1 0 1 0 0 -> 5 2 1 2 0 5 1 3 2 1 ,
  4 0 1 0 3 2 -> 2 2 2 4 3 4 3 3 5 3 ,
  4 4 3 0 5 5 -> 5 1 1 5 2 4 5 5 4 5 ,
  1 5 4 0 5 4 -> 4 2 2 4 1 0 5 5 2 2 ,
  5 0 1 0 1 4 -> 4 4 5 4 3 5 5 5 1 2 ,
  1 5 0 2 4 4 -> 5 4 3 2 1 2 1 5 3 4 ,
  0 3 2 3 0 5 0 -> 2 5 4 3 2 5 4 3 5 0 ,
  1 1 0 3 2 0 0 -> 5 0 3 0 0 0 4 0 2 0 ,
  4 0 1 4 3 0 3 -> 0 5 2 3 0 2 3 3 3 1 }


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

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


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

0 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 |
 \               /
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 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 |
 \               /
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 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 1 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 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 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 |
| 0 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 |
 \               /
5 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 1 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 4-rule system
{ 0 0 1 2 3 3 -> 3 4 4 3 5 0 3 3 0 3 ,
  4 3 0 2 3 0 -> 0 5 5 0 4 2 3 3 5 5 ,
  4 3 2 5 0 0 -> 3 0 1 5 4 5 4 3 1 0 ,
  2 1 5 1 2 3 2 -> 5 3 0 1 5 3 0 1 3 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 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 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

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