/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 { a->0, b->1, c->2 }, 
it remains to prove termination of the 3-rule system
{ 0 1 -> 1 0 0 0 ,
  1 0 -> 0 0 ,
  0 0 -> 0 2 1 }


The system was reversed.

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


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

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


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

After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (0,2)->3, (2,0)->4, (3,0)->5, (0,4)->6, (2,1)->7, (3,1)->8 },
it remains to prove termination of the 15-rule system
{ 0 1 2 -> 0 0 3 ,
  4 1 2 -> 4 0 3 ,
  5 1 2 -> 5 0 3 ,
  0 0 0 -> 1 2 4 0 ,
  0 0 1 -> 1 2 4 1 ,
  0 0 3 -> 1 2 4 3 ,
  0 0 6 -> 1 2 4 6 ,
  4 0 0 -> 7 2 4 0 ,
  4 0 1 -> 7 2 4 1 ,
  4 0 3 -> 7 2 4 3 ,
  4 0 6 -> 7 2 4 6 ,
  5 0 0 -> 8 2 4 0 ,
  5 0 1 -> 8 2 4 1 ,
  5 0 3 -> 8 2 4 3 ,
  5 0 6 -> 8 2 4 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 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 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 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.