/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:

a is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
C is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
B is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
A is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 10-rule system
{ a b c -> c b a ,
  C B A -> A B C ,
  b a C -> C a b ,
  c A B -> B A c ,
  A c b -> b c A ,
  B C a -> a C B ,
  b B -> ,
  B b -> ,
  c C -> ,
  C c -> }


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

a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
C is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
B is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
A is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 8-rule system
{ a b c -> c b a ,
  C B A -> A B C ,
  b a C -> C a b ,
  c A B -> B A c ,
  A c b -> b c A ,
  B C a -> a C B ,
  c C -> ,
  C c -> }


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

a is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
C is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
B is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
A is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ a b c -> c b a ,
  C B A -> A B C ,
  b a C -> C a b ,
  c A B -> B A c ,
  A c b -> b c A ,
  B C a -> a C B }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

a is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
b is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
c is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
C is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
B is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
A is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 5-rule system
{ C B A -> A B C ,
  b a C -> C a b ,
  c A B -> B A c ,
  A c b -> b c A ,
  B C a -> a C B }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

a is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
b is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
c is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
C is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
B is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
A is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 4-rule system
{ C B A -> A B C ,
  c A B -> B A c ,
  A c b -> b c A ,
  B C a -> a C B }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

a is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
b is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
c is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
C is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
B is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
A is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /

Remains to prove termination of the 3-rule system
{ C B A -> A B C ,
  c A B -> B A c ,
  B C a -> a C B }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

a is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
b is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
c is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
C is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
B is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
A is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 2-rule system
{ C B A -> A B C ,
  B C a -> a C B }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

a is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
b is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
c is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
C is interpreted by
 /       \
| 2 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
B is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
A is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /

Remains to prove termination of the 1-rule system
{ B C a -> a C B }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

a is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
b is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
c is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
C is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
B is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 1 0 |
 \       /
A is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 0-rule system
{ }


The system is trivially terminating.