/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

After renaming modulo { a12->0, a13->1, a14->2, a15->3, a16->4, a23->5, a24->6, a25->7, a26->8, a34->9, a35->10, a36->11, a45->12, a46->13, a56->14 }, 
it remains to prove termination of the 35-rule system
{ 0 0 -> ,
  1 1 -> ,
  2 2 -> ,
  3 3 -> ,
  4 4 -> ,
  5 5 -> ,
  6 6 -> ,
  7 7 -> ,
  8 8 -> ,
  9 9 -> ,
  10 10 -> ,
  11 11 -> ,
  12 12 -> ,
  13 13 -> ,
  14 14 -> ,
  1 -> 0 5 0 ,
  2 -> 0 5 9 5 0 ,
  3 -> 0 5 9 12 9 5 0 ,
  4 -> 0 5 9 12 14 12 9 5 0 ,
  6 -> 5 9 5 ,
  7 -> 5 9 12 9 5 ,
  8 -> 5 9 12 14 12 9 5 ,
  10 -> 9 12 9 ,
  11 -> 9 12 14 12 9 ,
  13 -> 12 14 12 ,
  0 5 0 5 0 5 -> ,
  5 9 5 9 5 9 -> ,
  9 12 9 12 9 12 -> ,
  12 14 12 14 12 14 -> ,
  0 9 -> 9 0 ,
  0 12 -> 12 0 ,
  0 14 -> 14 0 ,
  5 12 -> 12 5 ,
  5 14 -> 14 5 ,
  9 14 -> 14 9 }


The system was reversed.

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14 }, 
it remains to prove termination of the 35-rule system
{ 0 0 -> ,
  1 1 -> ,
  2 2 -> ,
  3 3 -> ,
  4 4 -> ,
  5 5 -> ,
  6 6 -> ,
  7 7 -> ,
  8 8 -> ,
  9 9 -> ,
  10 10 -> ,
  11 11 -> ,
  12 12 -> ,
  13 13 -> ,
  14 14 -> ,
  1 -> 0 5 0 ,
  2 -> 0 5 9 5 0 ,
  3 -> 0 5 9 12 9 5 0 ,
  4 -> 0 5 9 12 14 12 9 5 0 ,
  6 -> 5 9 5 ,
  7 -> 5 9 12 9 5 ,
  8 -> 5 9 12 14 12 9 5 ,
  10 -> 9 12 9 ,
  11 -> 9 12 14 12 9 ,
  13 -> 12 14 12 ,
  5 0 5 0 5 0 -> ,
  9 5 9 5 9 5 -> ,
  12 9 12 9 12 9 -> ,
  14 12 14 12 14 12 -> ,
  9 0 -> 0 9 ,
  12 0 -> 0 12 ,
  14 0 -> 0 14 ,
  12 5 -> 5 12 ,
  14 5 -> 5 14 ,
  14 9 -> 9 14 }


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 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 5->1, 9->2, 12->3, 14->4 }, 
it remains to prove termination of the 15-rule system
{ 0 0 -> ,
  1 1 -> ,
  2 2 -> ,
  3 3 -> ,
  4 4 -> ,
  1 0 1 0 1 0 -> ,
  2 1 2 1 2 1 -> ,
  3 2 3 2 3 2 -> ,
  4 3 4 3 4 3 -> ,
  2 0 -> 0 2 ,
  3 0 -> 0 3 ,
  4 0 -> 0 4 ,
  3 1 -> 1 3 ,
  4 1 -> 1 4 ,
  4 2 -> 2 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 1 |
| 0 1 |
 \   /

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


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

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


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

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