/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 { 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 0 0 -> ,
  1 1 1 1 -> ,
  2 2 2 2 -> ,
  3 3 3 3 -> ,
  4 4 4 4 -> ,
  5 5 5 5 -> ,
  6 6 6 6 -> ,
  7 7 7 7 -> ,
  8 8 8 8 -> ,
  9 9 9 9 -> ,
  10 10 10 10 -> ,
  11 11 11 11 -> ,
  12 12 12 12 -> ,
  13 13 13 13 -> ,
  14 14 14 14 -> ,
  1 1 -> 0 0 5 5 0 0 ,
  2 2 -> 0 0 5 5 9 9 5 5 0 0 ,
  3 3 -> 0 0 5 5 9 9 12 12 9 9 5 5 0 0 ,
  4 4 -> 0 0 5 5 9 9 12 12 14 14 12 12 9 9 5 5 0 0 ,
  6 6 -> 5 5 9 9 5 5 ,
  7 7 -> 5 5 9 9 12 12 9 9 5 5 ,
  8 8 -> 5 5 9 9 12 12 14 14 12 12 9 9 5 5 ,
  10 10 -> 9 9 12 12 9 9 ,
  11 11 -> 9 9 12 12 14 14 12 12 9 9 ,
  13 13 -> 12 12 14 14 12 12 ,
  0 0 5 5 0 0 5 5 0 0 5 5 -> ,
  5 5 9 9 5 5 9 9 5 5 9 9 -> ,
  9 9 12 12 9 9 12 12 9 9 12 12 -> ,
  12 12 14 14 12 12 14 14 12 12 14 14 -> ,
  0 0 9 9 -> 9 9 0 0 ,
  0 0 12 12 -> 12 12 0 0 ,
  0 0 14 14 -> 14 14 0 0 ,
  5 5 12 12 -> 12 12 5 5 ,
  5 5 14 14 -> 14 14 5 5 ,
  9 9 14 14 -> 14 14 9 9 }


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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (1,true)->3, (2,false)->4, (3,false)->5, (4,true)->6, (4,false)->7 },
it remains to prove termination of the 20-rule system
{ 0 1 2 2 -> 3 2 1 1 ,
  0 1 2 2 -> 3 1 1 ,
  0 1 2 2 -> 0 1 ,
  0 1 2 2 -> 0 ,
  0 1 4 4 -> 0 1 ,
  0 1 4 4 -> 0 ,
  0 1 5 5 -> 0 1 ,
  0 1 5 5 -> 0 ,
  6 7 4 4 -> 6 7 ,
  6 7 4 4 -> 6 ,
  6 7 5 5 -> 6 7 ,
  6 7 5 5 -> 6 ,
  3 2 5 5 -> 3 2 ,
  3 2 5 5 -> 3 ,
  1 1 2 2 ->= 2 2 1 1 ,
  1 1 4 4 ->= 4 4 1 1 ,
  1 1 5 5 ->= 5 5 1 1 ,
  7 7 4 4 ->= 4 4 7 7 ,
  7 7 5 5 ->= 5 5 7 7 ,
  2 2 5 5 ->= 5 5 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 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 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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

The system is trivially terminating.