/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES




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 |
 \   /
s is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
p is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


Applying context closure of depth 1 in the following form: System R over Sigma
maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
where fold(a_1,...,a_n) = (a_1,a_2)...(a_{n-1}a_{n})

Remains to prove termination of the 18-rule system
{ [f, f] [f, s] [s, f] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [f, p] [p, s] [s, f] -> [f, f] ,
  [f, f] [f, s] [s, s] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [f, p] [p, s] [s, s] -> [f, s] ,
  [f, f] [f, s] [s, p] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [f, p] [p, s] [s, p] -> [f, p] ,
  [s, f] [f, s] [s, f] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [s, p] [p, s] [s, f] -> [s, f] ,
  [s, f] [f, s] [s, s] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [s, p] [p, s] [s, s] -> [s, s] ,
  [s, f] [f, s] [s, p] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [s, p] [p, s] [s, p] -> [s, p] ,
  [p, f] [f, s] [s, f] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [p, p] [p, s] [s, f] -> [p, f] ,
  [p, f] [f, s] [s, s] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [p, p] [p, s] [s, s] -> [p, s] ,
  [p, f] [f, s] [s, p] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [p, p] [p, s] [s, p] -> [p, p] }



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

[f, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[f, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[f, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, p] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[p, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 13-rule system
{ [f, f] [f, s] [s, f] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [f, p] [p, s] [s, f] -> [f, f] ,
  [f, f] [f, s] [s, s] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [f, p] [p, s] [s, s] -> [f, s] ,
  [f, f] [f, s] [s, p] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [s, f] [f, s] [s, f] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [s, f] [f, s] [s, s] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [s, f] [f, s] [s, p] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [p, f] [f, s] [s, f] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [p, p] [p, s] [s, f] -> [p, f] ,
  [p, f] [f, s] [s, s] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [p, p] [p, s] [s, s] -> [p, s] ,
  [p, f] [f, s] [s, p] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, p] }


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

[f, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[f, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[f, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 11-rule system
{ [f, f] [f, s] [s, f] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [f, p] [p, s] [s, f] -> [f, f] ,
  [f, f] [f, s] [s, s] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [f, p] [p, s] [s, s] -> [f, s] ,
  [f, f] [f, s] [s, p] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [s, f] [f, s] [s, f] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [s, f] [f, s] [s, s] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [s, f] [f, s] [s, p] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [p, f] [f, s] [s, f] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [p, f] [f, s] [s, s] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [p, f] [f, s] [s, p] -> [p, s] [s, s] [s, f] [f, p] [p, s] [s, p] }


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

[f, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[f, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, f] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[f, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, s] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[s, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, f] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 8-rule system
{ [f, f] [f, s] [s, f] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [f, p] [p, s] [s, f] -> [f, f] ,
  [f, f] [f, s] [s, s] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [f, p] [p, s] [s, s] -> [f, s] ,
  [f, f] [f, s] [s, p] -> [f, s] [s, s] [s, f] [f, p] [p, s] [s, p] ,
  [s, f] [f, s] [s, f] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, f] ,
  [s, f] [f, s] [s, s] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, s] ,
  [s, f] [f, s] [s, p] -> [s, s] [s, s] [s, f] [f, p] [p, s] [s, p] }


The system was reversed.

Remains to prove termination of the 8-rule system
{ [s, f] [f, s] [f, f] -> [s, f] [p, s] [f, p] [s, f] [s, s] [f, s] ,
  [s, f] [p, s] [f, p] -> [f, f] ,
  [s, s] [f, s] [f, f] -> [s, s] [p, s] [f, p] [s, f] [s, s] [f, s] ,
  [s, s] [p, s] [f, p] -> [f, s] ,
  [s, p] [f, s] [f, f] -> [s, p] [p, s] [f, p] [s, f] [s, s] [f, s] ,
  [s, f] [f, s] [s, f] -> [s, f] [p, s] [f, p] [s, f] [s, s] [s, s] ,
  [s, s] [f, s] [s, f] -> [s, s] [p, s] [f, p] [s, f] [s, s] [s, s] ,
  [s, p] [f, s] [s, f] -> [s, p] [p, s] [f, p] [s, f] [s, s] [s, s] }


The dependency pairs transformation was applied.

Remains to prove termination of the 29-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([s, s],false) ([s, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([s, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([s, s],false) ([s, s],false) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([s, s],false) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, p],false) ([f, s],false) ([s, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }




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

([s, f],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([f, s],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([f, f],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([p, s],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([f, p],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, f],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, s],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, s],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, p],true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
([s, p],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 24-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([s, s],false) ([s, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([s, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, p],false) ([f, s],false) ([s, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([f, s],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([f, f],false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
([p, s],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([f, p],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, f],false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
([s, s],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, s],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, p],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([s, p],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 14-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, p],false) ([f, s],false) ([s, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) 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 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],true) 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 |
 \           /
([s, p],true) 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 |
 \           /
([s, p],false) 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 |
 \           /

Remains to prove termination of the 13-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, p],true) ([f, s],false) ([s, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) 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 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],true) 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 |
 \           /
([s, p],true) 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, p],false) 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 12-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],true) ([f, s],false) ([s, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) 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 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],true) 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 |
 \           /
([s, p],true) 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 |
 \           /
([s, p],false) 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 11-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([s, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) 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 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],true) 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, p],true) 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 |
 \           /
([s, p],false) 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 10-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, p],false) ([f, s],false) ([f, f],false) ->= ([s, p],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 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 |
 \           /
([s, s],true) 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 |
 \           /
([s, p],true) 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 |
 \           /
([s, p],false) 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 |
 \           /

Remains to prove termination of the 9-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, p],true) ([f, s],false) ([f, f],false) -> ([s, p],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 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 |
 \           /
([s, s],true) 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 |
 \           /
([s, p],true) 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, p],false) 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 8-rule system
{ ([s, f],true) ([f, s],false) ([f, f],false) -> ([s, f],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 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 |
 \           /
([s, s],true) 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 |
 \           /
([s, p],true) 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 |
 \           /
([s, p],false) 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 7-rule system
{ ([s, s],true) ([f, s],false) ([f, f],false) -> ([s, s],true) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


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

([s, f],true) 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 |
 \           /
([f, s],false) 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 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([f, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([p, s],false) 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 1 |
| 0 0 0 0 0 0 |
 \           /
([f, p],false) 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 |
 \           /
([s, f],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
([s, s],false) is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 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 |
 \           /
([s, s],true) 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, p],true) 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 |
 \           /
([s, p],false) 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 6-rule system
{ ([s, f],false) ([f, s],false) ([f, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, f],false) ([p, s],false) ([f, p],false) ->= ([f, f],false) ,
  ([s, s],false) ([f, s],false) ([f, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([f, s],false) ,
  ([s, s],false) ([p, s],false) ([f, p],false) ->= ([f, s],false) ,
  ([s, f],false) ([f, s],false) ([s, f],false) ->= ([s, f],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) ,
  ([s, s],false) ([f, s],false) ([s, f],false) ->= ([s, s],false) ([p, s],false) ([f, p],false) ([s, f],false) ([s, s],false) ([s, s],false) }


The system is trivially terminating.