/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 { q0->0, 0->1, 0'->2, q1->3, 1'->4, 1->5, q2->6, q3->7, b->8, q4->9 }, 
it remains to prove termination of the 16-rule system
{ 0 1 -> 2 3 ,
  3 1 -> 1 3 ,
  3 4 -> 4 3 ,
  1 3 5 -> 6 1 4 ,
  2 3 5 -> 6 2 4 ,
  4 3 5 -> 6 4 4 ,
  1 6 1 -> 6 1 1 ,
  2 6 1 -> 6 2 1 ,
  4 6 1 -> 6 4 1 ,
  1 6 4 -> 6 1 4 ,
  2 6 4 -> 6 2 4 ,
  4 6 4 -> 6 4 4 ,
  6 2 -> 2 0 ,
  0 4 -> 4 7 ,
  7 4 -> 4 7 ,
  7 8 -> 8 9 }


The system was reversed.

After renaming modulo { 1->0, 0->1, 3->2, 2->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, 
it remains to prove termination of the 16-rule system
{ 0 1 -> 2 3 ,
  0 2 -> 2 0 ,
  4 2 -> 2 4 ,
  5 2 0 -> 4 0 6 ,
  5 2 3 -> 4 3 6 ,
  5 2 4 -> 4 4 6 ,
  0 6 0 -> 0 0 6 ,
  0 6 3 -> 0 3 6 ,
  0 6 4 -> 0 4 6 ,
  4 6 0 -> 4 0 6 ,
  4 6 3 -> 4 3 6 ,
  4 6 4 -> 4 4 6 ,
  3 6 -> 1 3 ,
  4 1 -> 7 4 ,
  4 7 -> 7 4 ,
  8 7 -> 9 8 }


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

After renaming modulo { 0->0, 2->1, 4->2, 6->3, 3->4, 1->5, 7->6 }, 
it remains to prove termination of the 11-rule system
{ 0 1 -> 1 0 ,
  2 1 -> 1 2 ,
  0 3 0 -> 0 0 3 ,
  0 3 4 -> 0 4 3 ,
  0 3 2 -> 0 2 3 ,
  2 3 0 -> 2 0 3 ,
  2 3 4 -> 2 4 3 ,
  2 3 2 -> 2 2 3 ,
  4 3 -> 5 4 ,
  2 5 -> 6 2 ,
  2 6 -> 6 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 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, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 10-rule system
{ 0 1 -> 1 0 ,
  2 1 -> 1 2 ,
  0 3 0 -> 0 0 3 ,
  0 3 4 -> 0 4 3 ,
  0 3 2 -> 0 2 3 ,
  2 3 0 -> 2 0 3 ,
  2 3 4 -> 2 4 3 ,
  2 3 2 -> 2 2 3 ,
  4 3 -> 5 4 ,
  2 6 -> 6 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 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5 }, 
it remains to prove termination of the 9-rule system
{ 0 1 -> 1 0 ,
  2 1 -> 1 2 ,
  0 3 0 -> 0 0 3 ,
  0 3 4 -> 0 4 3 ,
  0 3 2 -> 0 2 3 ,
  2 3 0 -> 2 0 3 ,
  2 3 4 -> 2 4 3 ,
  2 3 2 -> 2 2 3 ,
  2 5 -> 5 2 }


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

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


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

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