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


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


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

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (3,false)->2, (3,true)->3, (4,false)->4, (2,false)->5, (0,false)->6 },
it remains to prove termination of the 21-rule system
{ 0 1 1 1 1 -> 0 1 1 1 ,
  0 1 1 1 2 -> 0 1 1 2 ,
  0 1 1 1 2 -> 3 ,
  0 1 1 1 4 -> 0 1 1 4 ,
  0 2 5 5 6 -> 0 2 6 1 ,
  0 2 5 5 6 -> 3 6 1 ,
  0 2 5 5 6 -> 0 1 ,
  3 5 6 1 1 -> 3 5 6 1 ,
  3 5 6 1 1 -> 0 1 ,
  3 5 6 1 2 -> 3 5 6 2 ,
  3 5 6 1 2 -> 0 2 ,
  3 5 6 1 2 -> 3 ,
  3 5 6 1 4 -> 3 5 6 4 ,
  3 5 6 1 4 -> 0 4 ,
  6 1 1 1 1 ->= 5 6 1 1 1 ,
  6 1 1 1 2 ->= 5 6 1 1 2 ,
  6 1 1 1 4 ->= 5 6 1 1 4 ,
  6 2 5 5 6 ->= 5 6 2 6 1 ,
  2 5 6 1 1 ->= 1 2 5 6 1 ,
  2 5 6 1 2 ->= 1 2 5 6 2 ,
  2 5 6 1 4 ->= 1 2 5 6 4 }


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 1 |
| 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 |
 \   /

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

The system is trivially terminating.