/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 |
 \   /
u is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
g is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
o is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 14-rule system
{ t u -> t c d ,
  d f -> f d ,
  d g -> u g ,
  f u -> u f ,
  d n -> d ,
  n u ->= u ,
  f ->= f n ,
  t ->= t c n ,
  c n ->= n c ,
  c o ->= o c ,
  c o ->= o ,
  c f ->= f c ,
  c u ->= u c ,
  c d ->= d 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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
u is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
d is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
f is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
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 0 |
 \     /

Remains to prove termination of the 13-rule system
{ t u -> t c d ,
  d f -> f d ,
  f u -> u f ,
  d n -> d ,
  n u ->= u ,
  f ->= f n ,
  t ->= t c n ,
  c n ->= n c ,
  c o ->= o c ,
  c o ->= o ,
  c f ->= f c ,
  c u ->= u c ,
  c d ->= d c }


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 |
 \   /
u is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
d is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
g is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
n is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
o is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 12-rule system
{ d f -> f d ,
  f u -> u f ,
  d n -> d ,
  n u ->= u ,
  f ->= f n ,
  t ->= t c n ,
  c n ->= n c ,
  c o ->= o c ,
  c o ->= o ,
  c f ->= f c ,
  c u ->= u c ,
  c d ->= d 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 |
 \     /
u 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 |
 \     /
d is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
f is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
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 0 |
 \     /

Remains to prove termination of the 11-rule system
{ d f -> f d ,
  d n -> d ,
  n u ->= u ,
  f ->= f n ,
  t ->= t c n ,
  c n ->= n c ,
  c o ->= o c ,
  c o ->= o ,
  c f ->= f c ,
  c u ->= u c ,
  c d ->= d 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 |
 \     /
u is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
d is interpreted by
 /     \
| 2 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
f is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
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 0 |
 \     /

Remains to prove termination of the 10-rule system
{ d n -> d ,
  n u ->= u ,
  f ->= f n ,
  t ->= t c n ,
  c n ->= n c ,
  c o ->= o c ,
  c o ->= o ,
  c f ->= f c ,
  c u ->= u c ,
  c d ->= d 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 |
 \     /
u is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
c is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
d is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
f is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
n is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
o is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 9-rule system
{ n u ->= u ,
  f ->= f n ,
  t ->= t c n ,
  c n ->= n c ,
  c o ->= o c ,
  c o ->= o ,
  c f ->= f c ,
  c u ->= u c ,
  c d ->= d c }


The system is trivially terminating.