/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


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

o is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
l is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
r is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
L is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
R is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ n l o -> r o ,
  L l o -> L r o ,
  o r n -> o l ,
  o r R -> o l R ,
  L ->= L n ,
  R ->= n R }


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

o is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
l is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
r is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
n is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
L is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
R 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 5-rule system
{ n l o -> r o ,
  o r n -> o l ,
  o r R -> o l R ,
  L ->= L n ,
  R ->= n R }


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

o is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
l is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
r is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
n is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
L is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
R is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /

Remains to prove termination of the 4-rule system
{ n l o -> r o ,
  o r n -> o l ,
  L ->= L n ,
  R ->= n R }


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

o is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
l is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
r is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
n is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
L is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
R 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 3-rule system
{ o r n -> o l ,
  L ->= L n ,
  R ->= n R }


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

o is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
l is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
r is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
L is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
R is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 2-rule system
{ L ->= L n ,
  R ->= n R }


The system is trivially terminating.