/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


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 12-rule system
{ [a, a] [a, a] -> [a, a] ,
  [a, a] [a, a] [a, a] -> [a, a] [a, b] [b, a] [a, b] [b, a] ,
  [a, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] ,
  [a, a] [a, b] -> [a, b] ,
  [a, a] [a, a] [a, b] -> [a, a] [a, b] [b, a] [a, b] [b, b] ,
  [a, b] [b, b] [b, b] [b, b] [b, b] -> [a, a] [a, b] ,
  [b, a] [a, a] -> [b, a] ,
  [b, a] [a, a] [a, a] -> [b, a] [a, b] [b, a] [a, b] [b, a] ,
  [b, b] [b, b] [b, b] [b, b] [b, a] -> [b, a] [a, a] ,
  [b, a] [a, b] -> [b, b] ,
  [b, a] [a, a] [a, b] -> [b, a] [a, b] [b, a] [a, b] [b, b] ,
  [b, b] [b, b] [b, b] [b, b] [b, b] -> [b, a] [a, b] }



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 2 |
| 0 1 |
 \   /
[a, b] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[b, a] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, b] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ [a, b] [b, b] [b, b] [b, b] [b, a] -> [a, a] [a, a] ,
  [a, a] [a, a] [a, b] -> [a, a] [a, b] [b, a] [a, b] [b, b] ,
  [b, a] [a, b] -> [b, b] ,
  [b, a] [a, a] [a, b] -> [b, a] [a, b] [b, a] [a, b] [b, b] }


The system was reversed.

Remains to prove termination of the 4-rule system
{ [b, a] [b, b] [b, b] [b, b] [a, b] -> [a, a] [a, a] ,
  [a, b] [a, a] [a, a] -> [b, b] [a, b] [b, a] [a, b] [a, a] ,
  [a, b] [b, a] -> [b, b] ,
  [a, b] [a, a] [b, a] -> [b, b] [a, b] [b, a] [a, b] [b, a] }


The dependency pairs transformation was applied.

Remains to prove termination of the 11-rule system
{ ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ,
  ([a, b],true) ([a, a],false) ([a, a],false) -> ([b, a],true) ([a, b],false) ([a, a],false) ,
  ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([a, a],false) ,
  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ,
  ([a, b],true) ([a, a],false) ([b, a],false) -> ([b, a],true) ([a, b],false) ([b, a],false) ,
  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ,
  ([a, b],true) ([a, a],false) ([b, a],false) -> ([b, a],true) ,
  ([b, a],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ,
  ([a, b],false) ([a, a],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ,
  ([a, b],false) ([b, a],false) ->= ([b, b],false) ,
  ([a, b],false) ([a, a],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) }




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

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

Remains to prove termination of the 8-rule system
{ ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([a, a],false) ,
  ([a, b],true) ([a, a],false) ([a, a],false) -> ([a, b],true) ([a, a],false) ,
  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ([a, b],false) ([b, a],false) ,
  ([a, b],true) ([a, a],false) ([b, a],false) -> ([a, b],true) ([b, a],false) ,
  ([b, a],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ,
  ([a, b],false) ([a, a],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ,
  ([a, b],false) ([b, a],false) ->= ([b, b],false) ,
  ([a, b],false) ([a, a],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) }


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

([a, b],true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([a, a],false) is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
([b, a],false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
([a, b],false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
([b, b],false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 4-rule system
{ ([b, a],false) ([b, b],false) ([b, b],false) ([b, b],false) ([a, b],false) ->= ([a, a],false) ([a, a],false) ,
  ([a, b],false) ([a, a],false) ([a, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([a, a],false) ,
  ([a, b],false) ([b, a],false) ->= ([b, b],false) ,
  ([a, b],false) ([a, a],false) ([b, a],false) ->= ([b, b],false) ([a, b],false) ([b, a],false) ([a, b],false) ([b, a],false) }


The system is trivially terminating.