/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:

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
* is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
# is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
$ is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ 0 0 * * -> * * 1 1 ,
  1 1 * * -> 0 0 # # ,
  # # 0 0 -> 0 0 # # ,
  # # 1 1 -> 1 1 # # ,
  # # $ $ -> * * $ $ }


The dependency pairs transformation was applied.

Remains to prove termination of the 19-rule system
{ (0,true) (0,false) (*,false) (*,false) -> (1,true) (1,false) ,
  (0,true) (0,false) (*,false) (*,false) -> (1,true) ,
  (1,true) (1,false) (*,false) (*,false) -> (0,true) (0,false) (#,false) (#,false) ,
  (1,true) (1,false) (*,false) (*,false) -> (0,true) (#,false) (#,false) ,
  (1,true) (1,false) (*,false) (*,false) -> (#,true) (#,false) ,
  (1,true) (1,false) (*,false) (*,false) -> (#,true) ,
  (#,true) (#,false) (0,false) (0,false) -> (0,true) (0,false) (#,false) (#,false) ,
  (#,true) (#,false) (0,false) (0,false) -> (0,true) (#,false) (#,false) ,
  (#,true) (#,false) (0,false) (0,false) -> (#,true) (#,false) ,
  (#,true) (#,false) (0,false) (0,false) -> (#,true) ,
  (#,true) (#,false) (1,false) (1,false) -> (1,true) (1,false) (#,false) (#,false) ,
  (#,true) (#,false) (1,false) (1,false) -> (1,true) (#,false) (#,false) ,
  (#,true) (#,false) (1,false) (1,false) -> (#,true) (#,false) ,
  (#,true) (#,false) (1,false) (1,false) -> (#,true) ,
  (0,false) (0,false) (*,false) (*,false) ->= (*,false) (*,false) (1,false) (1,false) ,
  (1,false) (1,false) (*,false) (*,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (0,false) (0,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (1,false) (1,false) ->= (1,false) (1,false) (#,false) (#,false) ,
  (#,false) (#,false) ($,false) ($,false) ->= (*,false) (*,false) ($,false) ($,false) }




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

(0,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(*,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(#,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(#,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
($,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 7-rule system
{ (0,true) (0,false) (*,false) (*,false) -> (1,true) (1,false) ,
  (1,true) (1,false) (*,false) (*,false) -> (0,true) (0,false) (#,false) (#,false) ,
  (0,false) (0,false) (*,false) (*,false) ->= (*,false) (*,false) (1,false) (1,false) ,
  (1,false) (1,false) (*,false) (*,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (0,false) (0,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (1,false) (1,false) ->= (1,false) (1,false) (#,false) (#,false) ,
  (#,false) (#,false) ($,false) ($,false) ->= (*,false) (*,false) ($,false) ($,false) }


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

(0,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(*,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(1,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(#,false) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
($,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 6-rule system
{ (1,true) (1,false) (*,false) (*,false) -> (0,true) (0,false) (#,false) (#,false) ,
  (0,false) (0,false) (*,false) (*,false) ->= (*,false) (*,false) (1,false) (1,false) ,
  (1,false) (1,false) (*,false) (*,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (0,false) (0,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (1,false) (1,false) ->= (1,false) (1,false) (#,false) (#,false) ,
  (#,false) (#,false) ($,false) ($,false) ->= (*,false) (*,false) ($,false) ($,false) }


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

(0,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(0,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(*,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(1,true) is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
(1,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(#,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
(#,true) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
($,false) is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 5-rule system
{ (0,false) (0,false) (*,false) (*,false) ->= (*,false) (*,false) (1,false) (1,false) ,
  (1,false) (1,false) (*,false) (*,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (0,false) (0,false) ->= (0,false) (0,false) (#,false) (#,false) ,
  (#,false) (#,false) (1,false) (1,false) ->= (1,false) (1,false) (#,false) (#,false) ,
  (#,false) (#,false) ($,false) ($,false) ->= (*,false) (*,false) ($,false) ($,false) }


The system is trivially terminating.