/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 3:

a is interpreted by
 /     \
| 1 2 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
b is interpreted by
 /     \
| 3 0 2 |
| 0 1 0 |
| 0 0 1 |
 \     /
d is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
f is interpreted by
 /     \
| 1 1 1 |
| 0 1 0 |
| 0 1 0 |
 \     /

Remains to prove termination of the 5-rule system
{ a b -> b d ,
  a c -> d d d ,
  b d -> a c b ,
  c f -> d d c ,
  d d -> f }


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 1 0 |
 \     /
d is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 4-rule system
{ a c -> d d d ,
  b d -> a c b ,
  c f -> d d c ,
  d d -> f }


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 0 |
| 0 1 0 |
| 0 2 1 |
 \     /
b is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 3 |
 \     /
d is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 2 1 |
 \     /

Remains to prove termination of the 3-rule system
{ a c -> d d d ,
  c f -> d d c ,
  d d -> f }


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 |
 \   /
d is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 2-rule system
{ c f -> d d c ,
  d d -> f }


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 |
 \       /
d is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 1 |
| 0 0 1 0 |
 \       /
c is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 1 0 |
 \       /
f is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 1 0 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 1-rule system
{ d d -> f }


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 |
 \   /
d is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


The system is trivially terminating.