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


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


YES




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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 33-rule system
{ a12 a12 a12 a12 -> ,
  a14 a14 a14 a14 -> ,
  a15 a15 a15 a15 -> ,
  a16 a16 a16 a16 -> ,
  a23 a23 a23 a23 -> ,
  a24 a24 a24 a24 -> ,
  a25 a25 a25 a25 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a14 a14 -> a12 a12 a23 a23 a34 a34 a23 a23 a12 a12 ,
  a15 a15 -> a12 a12 a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 a12 a12 ,
  a16 a16 -> a12 a12 a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 a12 a12 ,
  a24 a24 -> a23 a23 a34 a34 a23 a23 ,
  a25 a25 -> a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a12 a12 a23 a23 a12 a12 a23 a23 a12 a12 a23 a23 -> ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 31-rule system
{ a12 a12 a12 a12 -> ,
  a15 a15 a15 a15 -> ,
  a16 a16 a16 a16 -> ,
  a23 a23 a23 a23 -> ,
  a24 a24 a24 a24 -> ,
  a25 a25 a25 a25 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a15 a15 -> a12 a12 a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 a12 a12 ,
  a16 a16 -> a12 a12 a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 a12 a12 ,
  a24 a24 -> a23 a23 a34 a34 a23 a23 ,
  a25 a25 -> a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a12 a12 a23 a23 a12 a12 a23 a23 a12 a12 a23 a23 -> ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 29-rule system
{ a12 a12 a12 a12 -> ,
  a16 a16 a16 a16 -> ,
  a23 a23 a23 a23 -> ,
  a24 a24 a24 a24 -> ,
  a25 a25 a25 a25 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a16 a16 -> a12 a12 a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 a12 a12 ,
  a24 a24 -> a23 a23 a34 a34 a23 a23 ,
  a25 a25 -> a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a12 a12 a23 a23 a12 a12 a23 a23 a12 a12 a23 a23 -> ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 27-rule system
{ a12 a12 a12 a12 -> ,
  a23 a23 a23 a23 -> ,
  a24 a24 a24 a24 -> ,
  a25 a25 a25 a25 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a24 a24 -> a23 a23 a34 a34 a23 a23 ,
  a25 a25 -> a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a12 a12 a23 a23 a12 a12 a23 a23 a12 a12 a23 a23 -> ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 25-rule system
{ a23 a23 a23 a23 -> ,
  a24 a24 a24 a24 -> ,
  a25 a25 a25 a25 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a24 a24 -> a23 a23 a34 a34 a23 a23 ,
  a25 a25 -> a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 23-rule system
{ a23 a23 a23 a23 -> ,
  a25 a25 a25 a25 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a25 a25 -> a23 a23 a34 a34 a45 a45 a34 a34 a23 a23 ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 21-rule system
{ a23 a23 a23 a23 -> ,
  a26 a26 a26 a26 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a26 a26 -> a23 a23 a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 a23 a23 ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 19-rule system
{ a23 a23 a23 a23 -> ,
  a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a23 a23 a34 a34 a23 a23 a34 a34 a23 a23 a34 a34 -> ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 17-rule system
{ a34 a34 a34 a34 -> ,
  a35 a35 a35 a35 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a35 a35 -> a34 a34 a45 a45 a34 a34 ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 15-rule system
{ a34 a34 a34 a34 -> ,
  a36 a36 a36 a36 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a36 a36 -> a34 a34 a45 a45 a56 a56 a45 a45 a34 a34 ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 13-rule system
{ a34 a34 a34 a34 -> ,
  a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a34 a34 a45 a45 a34 a34 a45 a45 a34 a34 a45 a45 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ a45 a45 a45 a45 -> ,
  a46 a46 a46 a46 -> ,
  a56 a56 a56 a56 -> ,
  a46 a46 -> a45 a45 a56 a56 a45 a45 ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 9-rule system
{ a45 a45 a45 a45 -> ,
  a56 a56 a56 a56 -> ,
  a45 a45 a56 a56 a45 a45 a56 a56 a45 a45 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ a56 a56 a56 a56 -> ,
  a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


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

a12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a24 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a26 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a34 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a35 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a36 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a45 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a46 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
a56 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ a12 a12 a34 a34 -> a34 a34 a12 a12 ,
  a12 a12 a45 a45 -> a45 a45 a12 a12 ,
  a12 a12 a56 a56 -> a56 a56 a12 a12 ,
  a23 a23 a45 a45 -> a45 a45 a23 a23 ,
  a23 a23 a56 a56 -> a56 a56 a23 a23 ,
  a34 a34 a56 a56 -> a56 a56 a34 a34 }


The dependency pairs transformation was applied.

Remains to prove termination of the 20-rule system
{ (a12,true) (a12,false) (a34,false) (a34,false) -> (a34,true) (a34,false) (a12,false) (a12,false) ,
  (a12,true) (a12,false) (a34,false) (a34,false) -> (a34,true) (a12,false) (a12,false) ,
  (a12,true) (a12,false) (a34,false) (a34,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a34,false) (a34,false) -> (a12,true) ,
  (a12,true) (a12,false) (a45,false) (a45,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a45,false) (a45,false) -> (a12,true) ,
  (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) (a34,false) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) ,
  (a12,false) (a12,false) (a34,false) (a34,false) ->= (a34,false) (a34,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a12,false) (a12,false) ,
  (a23,false) (a23,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a23,false) (a23,false) ,
  (a23,false) (a23,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a23,false) (a23,false) ,
  (a34,false) (a34,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a34,false) (a34,false) }




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

(a12,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a12,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a45,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a56,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 18-rule system
{ (a12,true) (a12,false) (a34,false) (a34,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a34,false) (a34,false) -> (a12,true) ,
  (a12,true) (a12,false) (a45,false) (a45,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a45,false) (a45,false) -> (a12,true) ,
  (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) (a34,false) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) ,
  (a12,false) (a12,false) (a34,false) (a34,false) ->= (a34,false) (a34,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a12,false) (a12,false) ,
  (a23,false) (a23,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a23,false) (a23,false) ,
  (a23,false) (a23,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a23,false) (a23,false) ,
  (a34,false) (a34,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a34,false) (a34,false) }


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

(a12,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a12,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a34,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a45,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a56,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 15-rule system
{ (a12,true) (a12,false) (a34,false) (a34,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a45,false) (a45,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) (a12,false) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) (a34,false) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) ,
  (a12,false) (a12,false) (a34,false) (a34,false) ->= (a34,false) (a34,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a12,false) (a12,false) ,
  (a23,false) (a23,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a23,false) (a23,false) ,
  (a23,false) (a23,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a23,false) (a23,false) ,
  (a34,false) (a34,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a34,false) (a34,false) }


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

(a12,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a12,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a34,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a45,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a56,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 13-rule system
{ (a12,true) (a12,false) (a45,false) (a45,false) -> (a12,true) (a12,false) ,
  (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) (a12,false) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a45,false) (a45,false) -> (a23,true) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) (a34,false) ,
  (a12,false) (a12,false) (a34,false) (a34,false) ->= (a34,false) (a34,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a12,false) (a12,false) ,
  (a23,false) (a23,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a23,false) (a23,false) ,
  (a23,false) (a23,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a23,false) (a23,false) ,
  (a34,false) (a34,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a34,false) (a34,false) }


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

(a12,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a12,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a45,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a56,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 10-rule system
{ (a12,true) (a12,false) (a56,false) (a56,false) -> (a12,true) (a12,false) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) (a23,false) ,
  (a23,true) (a23,false) (a56,false) (a56,false) -> (a23,true) ,
  (a34,true) (a34,false) (a56,false) (a56,false) -> (a34,true) (a34,false) ,
  (a12,false) (a12,false) (a34,false) (a34,false) ->= (a34,false) (a34,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a12,false) (a12,false) ,
  (a23,false) (a23,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a23,false) (a23,false) ,
  (a23,false) (a23,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a23,false) (a23,false) ,
  (a34,false) (a34,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a34,false) (a34,false) }


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

(a12,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a12,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a34,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a45,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a56,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a23,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a23,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ (a12,false) (a12,false) (a34,false) (a34,false) ->= (a34,false) (a34,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a12,false) (a12,false) ,
  (a12,false) (a12,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a12,false) (a12,false) ,
  (a23,false) (a23,false) (a45,false) (a45,false) ->= (a45,false) (a45,false) (a23,false) (a23,false) ,
  (a23,false) (a23,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a23,false) (a23,false) ,
  (a34,false) (a34,false) (a56,false) (a56,false) ->= (a56,false) (a56,false) (a34,false) (a34,false) }


The system is trivially terminating.