/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 4:

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

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


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

b 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 |
 \     /
a is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
d is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /

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


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

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

Remains to prove termination of the 2-rule system
{ a b ->= d ,
  d ->= a b }


The system is trivially terminating.