/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES




The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

1 is interpreted by
 /     \
|  1 12 |
|  0  1 |
 \     /
4 is interpreted by
 /   \
| 1 8 |
| 0 1 |
 \   /
3 is interpreted by
 /     \
|  1 16 |
|  0  1 |
 \     /
2 is interpreted by
 /     \
|  1 18 |
|  0  1 |
 \     /
5 is interpreted by
 /     \
|  1 17 |
|  0  1 |
 \     /
6 is interpreted by
 /     \
|  1 15 |
|  0  1 |
 \     /

Remains to prove termination of the 7-rule system
{ 1 1 -> 4 3 ,
  1 2 -> 2 1 ,
  2 2 -> 1 1 1 ,
  3 3 -> 5 6 ,
  3 4 -> 1 1 ,
  4 4 -> 3 ,
  6 6 -> 2 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ 1 1 -> 4 3 ,
  1 2 -> 2 1 ,
  3 3 -> 5 6 ,
  3 4 -> 1 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ 1 1 -> 4 3 ,
  1 2 -> 2 1 ,
  3 4 -> 1 1 }


The system was reversed.

Remains to prove termination of the 3-rule system
{ 1 1 -> 3 4 ,
  2 1 -> 1 2 ,
  4 3 -> 1 1 }


The dependency pairs transformation was applied.

Remains to prove termination of the 8-rule system
{ (1,true) (1,false) -> (4,true) ,
  (2,true) (1,false) -> (1,true) (2,false) ,
  (2,true) (1,false) -> (2,true) ,
  (4,true) (3,false) -> (1,true) (1,false) ,
  (4,true) (3,false) -> (1,true) ,
  (1,false) (1,false) ->= (3,false) (4,false) ,
  (2,false) (1,false) ->= (1,false) (2,false) ,
  (4,false) (3,false) ->= (1,false) (1,false) }




The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(4,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(2,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(3,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(4,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (1,true) (1,false) -> (4,true) ,
  (2,true) (1,false) -> (2,true) ,
  (4,true) (3,false) -> (1,true) (1,false) ,
  (4,true) (3,false) -> (1,true) ,
  (1,false) (1,false) ->= (3,false) (4,false) ,
  (2,false) (1,false) ->= (1,false) (2,false) ,
  (4,false) (3,false) ->= (1,false) (1,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

(1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(4,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(2,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(2,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(3,false) is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
(4,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 3-rule system
{ (1,false) (1,false) ->= (3,false) (4,false) ,
  (2,false) (1,false) ->= (1,false) (2,false) ,
  (4,false) (3,false) ->= (1,false) (1,false) }


The system is trivially terminating.