/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 3:

f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
n is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
s is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /

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


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

f is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
s is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

f is interpreted by
 /     \
| 1 0 0 |
| 0 3 0 |
| 0 0 1 |
 \     /
n is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
c is interpreted by
 /     \
| 1 1 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
s is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


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

f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 2 |
 \     /
n is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
c is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
s is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


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

f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
n is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
s is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


The system is trivially terminating.