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


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YES


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 1 |
| 0 1 0 0 |
 \       /
b 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 13-rule system
{ a -> b ,
  a a -> a b a ,
  a b -> b b b ,
  a a b -> a b b a b ,
  a b a -> b a b b a ,
  a b b -> b b b b b ,
  a a a a -> a a a b a a a ,
  a a b a -> a b a b a b a ,
  a a b b -> a b b b a b b ,
  a b a a -> b a a b b a a ,
  a b a b -> b a b b b a b ,
  a b b a -> b b a b b b a ,
  a b b b -> b b b b b b b }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

a is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
 \         /
b is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /

Remains to prove termination of the 12-rule system
{ a -> b ,
  a a -> a b a ,
  a b -> b b b ,
  a a b -> a b b a b ,
  a b a -> b a b b a ,
  a b b -> b b b b b ,
  a a b a -> a b a b a b a ,
  a a b b -> a b b b a b b ,
  a b a a -> b a a b b a a ,
  a b a b -> b a b b b a b ,
  a b b a -> b b a b b b a ,
  a b b b -> b b b b b b b }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

a is interpreted by
 /         \
| 1 0 1 1 0 |
| 0 1 0 0 0 |
| 0 0 1 1 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
 \         /
b is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /

Remains to prove termination of the 11-rule system
{ a -> b ,
  a a -> a b a ,
  a b -> b b b ,
  a a b -> a b b a b ,
  a b a -> b a b b a ,
  a b b -> b b b b b ,
  a a b a -> a b a b a b a ,
  a a b b -> a b b b a b b ,
  a b a b -> b a b b b a b ,
  a b b a -> b b a b b b a ,
  a b b b -> b b b b b b b }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

a is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
b is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 7-rule system
{ a -> b ,
  a b -> b b b ,
  a b a -> b a b b a ,
  a b b -> b b b b b ,
  a b a b -> b a b b b a b ,
  a b b a -> b b a b b b a ,
  a b b b -> b b b b b b b }


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 |
 \   /

Remains to prove termination of the 3-rule system
{ a b a -> b a b b a ,
  a b a b -> b a b b b a b ,
  a b b a -> b b a b b b a }


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 1 0 0 |
| 0 1 0 0 |
 \       /
b 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 1-rule system
{ a b b a -> b b a b b b a }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

a is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
b is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /

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


The system is trivially terminating.