/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 2:

g is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
h is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
f is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
s is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
a is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ g h -> g f s ,
  f s s s -> h f s h ,
  f h -> h f s h ,
  h -> ,
  f f s s -> s s s f f ,
  b a -> a b }


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

g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
h is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
f 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 |
 \     /
b is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
a is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /

Remains to prove termination of the 5-rule system
{ g h -> g f s ,
  f s s s -> h f s h ,
  f h -> h f s h ,
  h -> ,
  f f s s -> s s s f f }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

g is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
h is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 1 1 |
| 0 0 0 0 1 |
 \         /
f is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 2 0 |
| 0 0 1 0 0 |
| 0 0 1 0 0 |
 \         /
s is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 1 1 1 0 |
 \         /
b is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
a is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /

Remains to prove termination of the 4-rule system
{ g h -> g f s ,
  f s s s -> h f s h ,
  f h -> h f s h ,
  h -> }


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

g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
h is interpreted by
 /     \
| 1 1 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
f is interpreted by
 /     \
| 1 0 2 |
| 0 1 0 |
| 1 1 2 |
 \     /
s is interpreted by
 /     \
| 1 1 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
b is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
a is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

Remains to prove termination of the 3-rule system
{ g h -> g f s ,
  f s s s -> h f s h ,
  f h -> h f s h }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

g is interpreted by
 /           \
| 1 0 0 0 0 1 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
h is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 1 0 0 |
 \           /
f is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
s is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 1 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
b is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
a is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

Remains to prove termination of the 2-rule system
{ g h -> g f s ,
  f h -> h f s h }


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

g is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
h is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
f 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 |
 \     /
b is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
a is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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


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

g is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
h is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
f is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
s is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
b is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
a 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.