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


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


YES


The system was reversed.

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


The dependency pairs transformation was applied.

Remains to prove termination of the 32-rule system
{ (s,true) (s,false) (a,false) (a,false) -> (a,true) (a,false) (s,false) (s,false) ,
  (s,true) (s,false) (a,false) (a,false) -> (a,true) (s,false) (s,false) ,
  (s,true) (s,false) (a,false) (a,false) -> (s,true) (s,false) ,
  (s,true) (s,false) (a,false) (a,false) -> (s,true) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (s,true) (b,false) (b,false) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) ,
  (s,false) (s,false) (a,false) (a,false) ->= (a,false) (a,false) (s,false) (s,false) ,
  (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (a,false) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) }




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

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

Remains to prove termination of the 24-rule system
{ (s,true) (s,false) (a,false) (a,false) -> (s,true) (s,false) ,
  (s,true) (s,false) (a,false) (a,false) -> (s,true) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (s,true) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) ,
  (s,false) (s,false) (a,false) (a,false) ->= (a,false) (a,false) (s,false) (s,false) ,
  (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (a,false) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) }


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

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

Remains to prove termination of the 22-rule system
{ (s,true) (s,false) (a,false) (a,false) -> (s,true) (s,false) ,
  (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (s,true) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (a,false) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) (a,false) ,
  (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (a,true) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (a,false) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (b,false) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) (b,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (b,true) ,
  (s,false) (s,false) (a,false) (a,false) ->= (a,false) (a,false) (s,false) (s,false) ,
  (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (a,false) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) }


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

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

Remains to prove termination of the 6-rule system
{ (b,true) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) -> (b,true) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (s,false) (s,false) (a,false) (a,false) ->= (a,false) (a,false) (s,false) (s,false) ,
  (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (a,false) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

(s,true) is interpreted by
 /                 \
| 1 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 |
| 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 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,false) is interpreted by
 /                 \
| 1 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 |
| 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 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 |
 \                 /
(a,false) is interpreted by
 /                 \
| 1 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 |
| 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 |
| 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 |
 \                 /
(a,true) is interpreted by
 /                 \
| 1 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 |
| 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 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 |
 \                 /
(b,false) is interpreted by
 /                 \
| 1 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 |
| 0 0 0 1 0 0 0 0 0 |
| 0 0 1 0 1 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 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 1 |
| 0 1 0 0 0 0 0 0 0 |
 \                 /
(b,true) is interpreted by
 /                 \
| 1 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 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 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 5-rule system
{ (a,true) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) -> (a,true) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ,
  (s,false) (s,false) (a,false) (a,false) ->= (a,false) (a,false) (s,false) (s,false) ,
  (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (a,false) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

(s,true) is interpreted by
 /                 \
| 1 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 |
| 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 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,false) is interpreted by
 /                 \
| 1 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 |
| 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 0 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 |
 \                 /
(a,false) is interpreted by
 /                 \
| 1 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 0 |
| 0 0 0 1 0 0 0 0 0 |
| 0 0 1 0 1 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 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 1 |
| 0 1 0 0 0 0 0 0 0 |
 \                 /
(a,true) is interpreted by
 /                 \
| 1 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 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 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
 \                 /
(b,false) is interpreted by
 /                 \
| 1 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 |
| 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 |
| 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 |
 \                 /
(b,true) is interpreted by
 /                 \
| 1 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 |
| 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 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 4-rule system
{ (s,false) (s,false) (a,false) (a,false) ->= (a,false) (a,false) (s,false) (s,false) ,
  (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (a,false) (a,false) (s,false) (s,false) (b,false) (b,false) (a,false) (a,false) ,
  (b,false) (b,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) ->= (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ,
  (a,false) (a,false) (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) ->= (a,false) (a,false) (b,false) (b,false) (a,false) (a,false) (b,false) (b,false) }


The system is trivially terminating.