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


The system was reversed.

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


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

After renaming modulo { 0->0, 1->1, 5->2 },
it remains to prove termination of the 4-rule system
{ 0 -> 1 ,
  0 0 -> 0 ,
  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 -> 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 ,
  1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 -> 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 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 19 |
|  0  1 |
 \     /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /     \
|  1 37 |
|  0  1 |
 \     /

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

The system is trivially terminating.