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


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


YES




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

a is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
b is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
C is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
c is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
A is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
B is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ B a a a -> c A A A ,
  A A A b -> a a a C ,
  C b b b -> a B B B ,
  B B B c -> b b b A ,
  A c c c -> b C C C ,
  C C C a -> c c c B }


The system was reversed.

Remains to prove termination of the 6-rule system
{ a a a B -> A A A c ,
  b A A A -> C a a a ,
  b b b C -> B B B a ,
  c B B B -> A b b b ,
  c c c A -> C C C b ,
  a C C C -> B c c c }


The dependency pairs transformation was applied.

Remains to prove termination of the 18-rule system
{ (a,true) (a,false) (a,false) (B,false) -> (c,true) ,
  (b,true) (A,false) (A,false) (A,false) -> (a,true) (a,false) (a,false) ,
  (b,true) (A,false) (A,false) (A,false) -> (a,true) (a,false) ,
  (b,true) (A,false) (A,false) (A,false) -> (a,true) ,
  (b,true) (b,false) (b,false) (C,false) -> (a,true) ,
  (c,true) (B,false) (B,false) (B,false) -> (b,true) (b,false) (b,false) ,
  (c,true) (B,false) (B,false) (B,false) -> (b,true) (b,false) ,
  (c,true) (B,false) (B,false) (B,false) -> (b,true) ,
  (c,true) (c,false) (c,false) (A,false) -> (b,true) ,
  (a,true) (C,false) (C,false) (C,false) -> (c,true) (c,false) (c,false) ,
  (a,true) (C,false) (C,false) (C,false) -> (c,true) (c,false) ,
  (a,true) (C,false) (C,false) (C,false) -> (c,true) ,
  (a,false) (a,false) (a,false) (B,false) ->= (A,false) (A,false) (A,false) (c,false) ,
  (b,false) (A,false) (A,false) (A,false) ->= (C,false) (a,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (C,false) ->= (B,false) (B,false) (B,false) (a,false) ,
  (c,false) (B,false) (B,false) (B,false) ->= (A,false) (b,false) (b,false) (b,false) ,
  (c,false) (c,false) (c,false) (A,false) ->= (C,false) (C,false) (C,false) (b,false) ,
  (a,false) (C,false) (C,false) (C,false) ->= (B,false) (c,false) (c,false) (c,false) }




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

(a,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(B,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(A,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(C,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (b,true) (A,false) (A,false) (A,false) -> (a,true) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (B,false) ->= (A,false) (A,false) (A,false) (c,false) ,
  (b,false) (A,false) (A,false) (A,false) ->= (C,false) (a,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (C,false) ->= (B,false) (B,false) (B,false) (a,false) ,
  (c,false) (B,false) (B,false) (B,false) ->= (A,false) (b,false) (b,false) (b,false) ,
  (c,false) (c,false) (c,false) (A,false) ->= (C,false) (C,false) (C,false) (b,false) ,
  (a,false) (C,false) (C,false) (C,false) ->= (B,false) (c,false) (c,false) (c,false) }


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

(a,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(a,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(B,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(A,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(b,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(C,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(c,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ (a,false) (a,false) (a,false) (B,false) ->= (A,false) (A,false) (A,false) (c,false) ,
  (b,false) (A,false) (A,false) (A,false) ->= (C,false) (a,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (C,false) ->= (B,false) (B,false) (B,false) (a,false) ,
  (c,false) (B,false) (B,false) (B,false) ->= (A,false) (b,false) (b,false) (b,false) ,
  (c,false) (c,false) (c,false) (A,false) ->= (C,false) (C,false) (C,false) (b,false) ,
  (a,false) (C,false) (C,false) (C,false) ->= (B,false) (c,false) (c,false) (c,false) }


The system is trivially terminating.