/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:

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

Remains to prove termination of the 8-rule system
{ t f -> t c n ,
  n f -> f n ,
  o f -> f o ,
  n s -> f s ,
  c f -> f c ,
  c n -> n c ,
  c o -> o c ,
  c o -> o }


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

t is interpreted by
 /       \
| 1 0 0 1 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
f is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 1 0 |
 \       /
c 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 1 0 |
| 0 0 1 0 |
 \       /
o is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
s is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 7-rule system
{ t f -> t c n ,
  n f -> f n ,
  o f -> f o ,
  c f -> f c ,
  c n -> n c ,
  c o -> o c ,
  c o -> o }


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

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

Remains to prove termination of the 6-rule system
{ n f -> f n ,
  o f -> f o ,
  c f -> f c ,
  c n -> n c ,
  c o -> o c ,
  c o -> o }


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

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

Remains to prove termination of the 5-rule system
{ n f -> f n ,
  o f -> f o ,
  c f -> f c ,
  c n -> n c ,
  c o -> o c }


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

t is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
c 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 |
 \     /
o is interpreted by
 /     \
| 1 0 0 |
| 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 4-rule system
{ o f -> f o ,
  c f -> f c ,
  c n -> n c ,
  c o -> o c }


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

t is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
f 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 |
 \     /
n is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
o is interpreted by
 /     \
| 2 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 3-rule system
{ c f -> f c ,
  c n -> n c ,
  c o -> o c }


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

t is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
c is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
n is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
o is interpreted by
 /     \
| 1 0 0 |
| 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 2-rule system
{ c n -> n c ,
  c o -> o c }


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

t 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 |
 \     /
c is interpreted by
 /     \
| 2 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
n is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
o is interpreted by
 /     \
| 1 0 0 |
| 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
{ c o -> o c }


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

t 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 |
 \     /
c is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
n is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
o is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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.