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


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


YES


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 27-rule system
{ [a, a] [a, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
  [a, a] [a, b] [b, c] [c, a] -> [a, b] [b, c] [c, b] [b, c] [c, a] ,
  [a, a] [a, b] [b, c] [c, a] -> [a, c] [c, b] [b, c] [c, a] [a, a] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, a] [a, a] [a, b] [b, b] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, b] [b, c] [c, b] [b, c] [c, b] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, c] [c, b] [b, c] [c, a] [a, b] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, a] [a, a] [a, b] [b, c] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, b] [b, c] [c, b] [b, c] [c, c] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, c] [c, b] [b, c] [c, a] [a, c] ,
  [b, a] [a, b] [b, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
  [b, a] [a, b] [b, c] [c, a] -> [b, b] [b, c] [c, b] [b, c] [c, a] ,
  [b, a] [a, b] [b, c] [c, a] -> [b, c] [c, b] [b, c] [c, a] [a, a] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, b] [b, c] [c, b] [b, c] [c, b] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, c] [c, b] [b, c] [c, a] [a, b] ,
  [b, a] [a, b] [b, c] [c, c] -> [b, a] [a, a] [a, b] [b, c] ,
  [b, a] [a, b] [b, c] [c, c] -> [b, b] [b, c] [c, b] [b, c] [c, c] ,
  [b, a] [a, b] [b, c] [c, c] -> [b, c] [c, b] [b, c] [c, a] [a, c] ,
  [c, a] [a, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
  [c, a] [a, b] [b, c] [c, a] -> [c, b] [b, c] [c, b] [b, c] [c, a] ,
  [c, a] [a, b] [b, c] [c, a] -> [c, c] [c, b] [b, c] [c, a] [a, a] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, b] [b, c] [c, b] [b, c] [c, b] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, c] [c, b] [b, c] [c, a] [a, b] ,
  [c, a] [a, b] [b, c] [c, c] -> [c, a] [a, a] [a, b] [b, c] ,
  [c, a] [a, b] [b, c] [c, c] -> [c, b] [b, c] [c, b] [b, c] [c, c] ,
  [c, a] [a, b] [b, c] [c, c] -> [c, c] [c, b] [b, c] [c, a] [a, c] }



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

[a, a] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[a, b] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[b, c] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[c, a] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, a] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[c, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[a, c] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[c, c] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 15-rule system
{ [a, a] [a, b] [b, c] [c, a] -> [a, a] [a, a] [a, b] [b, a] ,
  [a, a] [a, b] [b, c] [c, a] -> [a, b] [b, c] [c, b] [b, c] [c, a] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, a] [a, a] [a, b] [b, b] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, b] [b, c] [c, b] [b, c] [c, b] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, c] [c, b] [b, c] [c, a] [a, b] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, a] [a, a] [a, b] [b, c] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, b] [b, c] [c, b] [b, c] [c, c] ,
  [b, a] [a, b] [b, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, c] [c, b] [b, c] [c, a] [a, b] ,
  [b, a] [a, b] [b, c] [c, c] -> [b, a] [a, a] [a, b] [b, c] ,
  [c, a] [a, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, c] [c, b] [b, c] [c, a] [a, b] ,
  [c, a] [a, b] [b, c] [c, c] -> [c, a] [a, a] [a, b] [b, c] }


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

[a, a] is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
[a, b] is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
[b, c] is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
[c, 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 1 0 0 0 |
 \         /
[b, 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 |
 \         /
[c, 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, c] 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 |
 \         /
[b, 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 |
 \         /
[c, c] is interpreted by
 /         \
| 1 0 0 0 1 |
| 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 13-rule system
{ [a, a] [a, b] [b, c] [c, b] -> [a, a] [a, a] [a, b] [b, b] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, b] [b, c] [c, b] [b, c] [c, b] ,
  [a, a] [a, b] [b, c] [c, b] -> [a, c] [c, b] [b, c] [c, a] [a, b] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, a] [a, a] [a, b] [b, c] ,
  [a, a] [a, b] [b, c] [c, c] -> [a, b] [b, c] [c, b] [b, c] [c, c] ,
  [b, a] [a, b] [b, c] [c, a] -> [b, a] [a, a] [a, b] [b, a] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, a] [a, a] [a, b] [b, b] ,
  [b, a] [a, b] [b, c] [c, b] -> [b, c] [c, b] [b, c] [c, a] [a, b] ,
  [b, a] [a, b] [b, c] [c, c] -> [b, a] [a, a] [a, b] [b, c] ,
  [c, a] [a, b] [b, c] [c, a] -> [c, a] [a, a] [a, b] [b, a] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, a] [a, a] [a, b] [b, b] ,
  [c, a] [a, b] [b, c] [c, b] -> [c, c] [c, b] [b, c] [c, a] [a, b] ,
  [c, a] [a, b] [b, c] [c, c] -> [c, a] [a, a] [a, b] [b, c] }


The system was reversed.

Remains to prove termination of the 13-rule system
{ [c, b] [b, c] [a, b] [a, a] -> [b, b] [a, b] [a, a] [a, a] ,
  [c, b] [b, c] [a, b] [a, a] -> [c, b] [b, c] [c, b] [b, c] [a, b] ,
  [c, b] [b, c] [a, b] [a, a] -> [a, b] [c, a] [b, c] [c, b] [a, c] ,
  [c, c] [b, c] [a, b] [a, a] -> [b, c] [a, b] [a, a] [a, a] ,
  [c, c] [b, c] [a, b] [a, a] -> [c, c] [b, c] [c, b] [b, c] [a, b] ,
  [c, a] [b, c] [a, b] [b, a] -> [b, a] [a, b] [a, a] [b, a] ,
  [c, b] [b, c] [a, b] [b, a] -> [b, b] [a, b] [a, a] [b, a] ,
  [c, b] [b, c] [a, b] [b, a] -> [a, b] [c, a] [b, c] [c, b] [b, c] ,
  [c, c] [b, c] [a, b] [b, a] -> [b, c] [a, b] [a, a] [b, a] ,
  [c, a] [b, c] [a, b] [c, a] -> [b, a] [a, b] [a, a] [c, a] ,
  [c, b] [b, c] [a, b] [c, a] -> [b, b] [a, b] [a, a] [c, a] ,
  [c, b] [b, c] [a, b] [c, a] -> [a, b] [c, a] [b, c] [c, b] [c, c] ,
  [c, c] [b, c] [a, b] [c, a] -> [b, c] [a, b] [a, a] [c, a] }


The dependency pairs transformation was applied.

Remains to prove termination of the 27-rule system
{ ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, a],true) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([a, c],false) ,
  ([c, c],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, c],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, c],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([b, a],false) -> ([c, a],true) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([b, a],false) -> ([c, b],true) ([b, c],false) ,
  ([c, a],true) ([b, c],false) ([a, b],false) ([c, a],false) -> ([c, a],true) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([c, a],false) -> ([c, a],true) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([c, a],false) -> ([c, a],true) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([c, a],false) -> ([c, b],true) ([c, c],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([c, a],false) -> ([c, c],true) ,
  ([c, c],true) ([b, c],false) ([a, b],false) ([c, a],false) -> ([c, a],true) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([c, a],false) }




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

([c, b],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([b, c],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([a, b],false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
([a, a],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, b],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, a],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([a, c],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, c],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([b, a],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, a],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, c],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([b, b],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 17-rule system
{ ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, c],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, c],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, c],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([c, a],false) }


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

([c, b],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([b, c],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([a, b],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([a, a],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, b],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, a],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([a, c],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, c],true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
([b, a],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, a],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([c, c],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([b, b],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 16-rule system
{ ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, c],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, c],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([c, a],false) }


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

([c, b],true) 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 |
 \         /
([b, c],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([a, b],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
([a, a],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
([c, b],false) 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 |
 \         /
([c, a],true) 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, c],false) 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 |
 \         /
([c, c],true) is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([b, a],false) 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 |
 \         /
([c, a],false) 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 |
 \         /
([c, c],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([b, b],false) 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 15-rule system
{ ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, c],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([c, a],false) }


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

([c, b],true) 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 |
 \         /
([b, c],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([a, b],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
([a, a],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
([c, b],false) 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 |
 \         /
([c, a],true) 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, c],false) 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 |
 \         /
([c, c],true) 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 |
 \         /
([b, a],false) 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 |
 \         /
([c, a],false) is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([c, c],false) is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([b, b],false) 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 13-rule system
{ ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],true) ([b, c],false) ([a, b],false) ([a, a],false) -> ([c, b],true) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([c, a],false) }


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

([c, b],true) is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([b, c],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([a, b],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
([a, a],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 1 |
 \         /
([c, b],false) 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 |
 \         /
([c, a],true) 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, c],false) 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 |
 \         /
([c, c],true) 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 |
 \         /
([b, a],false) 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 |
 \         /
([c, a],false) 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 |
 \         /
([c, c],false) is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
([b, b],false) 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 11-rule system
{ ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([a, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([c, b],false) ([b, c],false) ([c, b],false) ([b, c],false) ([a, b],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([a, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([a, c],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([b, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([b, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([b, a],false) ,
  ([c, a],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, a],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, b],false) ([a, b],false) ([a, a],false) ([c, a],false) ,
  ([c, b],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([a, b],false) ([c, a],false) ([b, c],false) ([c, b],false) ([c, c],false) ,
  ([c, c],false) ([b, c],false) ([a, b],false) ([c, a],false) ->= ([b, c],false) ([a, b],false) ([a, a],false) ([c, a],false) }


The system is trivially terminating.