/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 150-rule system
{ [b, b] [b, p] [p, b] [b, b] -> [b, b] [b, q] [q, b] [b, b] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [b, p] [p, b] ,
  [b, q] [q, b] ->= [b, 0] [0, q] [q, 0] [0, b] ,
  [b, q] [q, b] ->= [b, 1] [1, q] [q, 1] [1, b] ,
  [b, q] [q, b] ->= [b, 0] [0, p] [p, 0] [0, b] ,
  [b, q] [q, b] ->= [b, 1] [1, p] [p, 1] [1, b] ,
  [b, b] [b, p] [p, b] [b, p] -> [b, b] [b, q] [q, b] [b, p] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [b, p] [p, p] ,
  [b, q] [q, p] ->= [b, 0] [0, q] [q, 0] [0, p] ,
  [b, q] [q, p] ->= [b, 1] [1, q] [q, 1] [1, p] ,
  [b, q] [q, p] ->= [b, 0] [0, p] [p, 0] [0, p] ,
  [b, q] [q, p] ->= [b, 1] [1, p] [p, 1] [1, p] ,
  [b, b] [b, p] [p, b] [b, q] -> [b, b] [b, q] [q, b] [b, q] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [b, p] [p, q] ,
  [b, q] [q, q] ->= [b, 0] [0, q] [q, 0] [0, q] ,
  [b, q] [q, q] ->= [b, 1] [1, q] [q, 1] [1, q] ,
  [b, q] [q, q] ->= [b, 0] [0, p] [p, 0] [0, q] ,
  [b, q] [q, q] ->= [b, 1] [1, p] [p, 1] [1, q] ,
  [b, b] [b, p] [p, b] [b, 1] -> [b, b] [b, q] [q, b] [b, 1] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [b, p] [p, 1] ,
  [b, q] [q, 1] ->= [b, 0] [0, q] [q, 0] [0, 1] ,
  [b, q] [q, 1] ->= [b, 1] [1, q] [q, 1] [1, 1] ,
  [b, q] [q, 1] ->= [b, 0] [0, p] [p, 0] [0, 1] ,
  [b, q] [q, 1] ->= [b, 1] [1, p] [p, 1] [1, 1] ,
  [b, b] [b, p] [p, b] [b, 0] -> [b, b] [b, q] [q, b] [b, 0] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [b, p] [p, 0] ,
  [b, q] [q, 0] ->= [b, 0] [0, q] [q, 0] [0, 0] ,
  [b, q] [q, 0] ->= [b, 1] [1, q] [q, 1] [1, 0] ,
  [b, q] [q, 0] ->= [b, 0] [0, p] [p, 0] [0, 0] ,
  [b, q] [q, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] ,
  [p, b] [b, p] [p, b] [b, b] -> [p, b] [b, q] [q, b] [b, b] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [p, p] [p, b] ,
  [p, q] [q, b] ->= [p, 0] [0, q] [q, 0] [0, b] ,
  [p, q] [q, b] ->= [p, 1] [1, q] [q, 1] [1, b] ,
  [p, q] [q, b] ->= [p, 0] [0, p] [p, 0] [0, b] ,
  [p, q] [q, b] ->= [p, 1] [1, p] [p, 1] [1, b] ,
  [p, b] [b, p] [p, b] [b, p] -> [p, b] [b, q] [q, b] [b, p] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [p, p] [p, p] ,
  [p, q] [q, p] ->= [p, 0] [0, q] [q, 0] [0, p] ,
  [p, q] [q, p] ->= [p, 1] [1, q] [q, 1] [1, p] ,
  [p, q] [q, p] ->= [p, 0] [0, p] [p, 0] [0, p] ,
  [p, q] [q, p] ->= [p, 1] [1, p] [p, 1] [1, p] ,
  [p, b] [b, p] [p, b] [b, q] -> [p, b] [b, q] [q, b] [b, q] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [p, p] [p, q] ,
  [p, q] [q, q] ->= [p, 0] [0, q] [q, 0] [0, q] ,
  [p, q] [q, q] ->= [p, 1] [1, q] [q, 1] [1, q] ,
  [p, q] [q, q] ->= [p, 0] [0, p] [p, 0] [0, q] ,
  [p, q] [q, q] ->= [p, 1] [1, p] [p, 1] [1, q] ,
  [p, b] [b, p] [p, b] [b, 1] -> [p, b] [b, q] [q, b] [b, 1] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [p, p] [p, 1] ,
  [p, q] [q, 1] ->= [p, 0] [0, q] [q, 0] [0, 1] ,
  [p, q] [q, 1] ->= [p, 1] [1, q] [q, 1] [1, 1] ,
  [p, q] [q, 1] ->= [p, 0] [0, p] [p, 0] [0, 1] ,
  [p, q] [q, 1] ->= [p, 1] [1, p] [p, 1] [1, 1] ,
  [p, b] [b, p] [p, b] [b, 0] -> [p, b] [b, q] [q, b] [b, 0] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [p, p] [p, 0] ,
  [p, q] [q, 0] ->= [p, 0] [0, q] [q, 0] [0, 0] ,
  [p, q] [q, 0] ->= [p, 1] [1, q] [q, 1] [1, 0] ,
  [p, q] [q, 0] ->= [p, 0] [0, p] [p, 0] [0, 0] ,
  [p, q] [q, 0] ->= [p, 1] [1, p] [p, 1] [1, 0] ,
  [q, b] [b, p] [p, b] [b, b] -> [q, b] [b, q] [q, b] [b, b] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [q, p] [p, b] ,
  [q, q] [q, b] ->= [q, 0] [0, q] [q, 0] [0, b] ,
  [q, q] [q, b] ->= [q, 1] [1, q] [q, 1] [1, b] ,
  [q, q] [q, b] ->= [q, 0] [0, p] [p, 0] [0, b] ,
  [q, q] [q, b] ->= [q, 1] [1, p] [p, 1] [1, b] ,
  [q, b] [b, p] [p, b] [b, p] -> [q, b] [b, q] [q, b] [b, p] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [q, p] [p, p] ,
  [q, q] [q, p] ->= [q, 0] [0, q] [q, 0] [0, p] ,
  [q, q] [q, p] ->= [q, 1] [1, q] [q, 1] [1, p] ,
  [q, q] [q, p] ->= [q, 0] [0, p] [p, 0] [0, p] ,
  [q, q] [q, p] ->= [q, 1] [1, p] [p, 1] [1, p] ,
  [q, b] [b, p] [p, b] [b, q] -> [q, b] [b, q] [q, b] [b, q] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [q, p] [p, q] ,
  [q, q] [q, q] ->= [q, 0] [0, q] [q, 0] [0, q] ,
  [q, q] [q, q] ->= [q, 1] [1, q] [q, 1] [1, q] ,
  [q, q] [q, q] ->= [q, 0] [0, p] [p, 0] [0, q] ,
  [q, q] [q, q] ->= [q, 1] [1, p] [p, 1] [1, q] ,
  [q, b] [b, p] [p, b] [b, 1] -> [q, b] [b, q] [q, b] [b, 1] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [q, p] [p, 1] ,
  [q, q] [q, 1] ->= [q, 0] [0, q] [q, 0] [0, 1] ,
  [q, q] [q, 1] ->= [q, 1] [1, q] [q, 1] [1, 1] ,
  [q, q] [q, 1] ->= [q, 0] [0, p] [p, 0] [0, 1] ,
  [q, q] [q, 1] ->= [q, 1] [1, p] [p, 1] [1, 1] ,
  [q, b] [b, p] [p, b] [b, 0] -> [q, b] [b, q] [q, b] [b, 0] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [q, p] [p, 0] ,
  [q, q] [q, 0] ->= [q, 0] [0, q] [q, 0] [0, 0] ,
  [q, q] [q, 0] ->= [q, 1] [1, q] [q, 1] [1, 0] ,
  [q, q] [q, 0] ->= [q, 0] [0, p] [p, 0] [0, 0] ,
  [q, q] [q, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] ,
  [1, b] [b, p] [p, b] [b, b] -> [1, b] [b, q] [q, b] [b, b] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [1, p] [p, b] ,
  [1, q] [q, b] ->= [1, 0] [0, q] [q, 0] [0, b] ,
  [1, q] [q, b] ->= [1, 1] [1, q] [q, 1] [1, b] ,
  [1, q] [q, b] ->= [1, 0] [0, p] [p, 0] [0, b] ,
  [1, q] [q, b] ->= [1, 1] [1, p] [p, 1] [1, b] ,
  [1, b] [b, p] [p, b] [b, p] -> [1, b] [b, q] [q, b] [b, p] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [1, p] [p, p] ,
  [1, q] [q, p] ->= [1, 0] [0, q] [q, 0] [0, p] ,
  [1, q] [q, p] ->= [1, 1] [1, q] [q, 1] [1, p] ,
  [1, q] [q, p] ->= [1, 0] [0, p] [p, 0] [0, p] ,
  [1, q] [q, p] ->= [1, 1] [1, p] [p, 1] [1, p] ,
  [1, b] [b, p] [p, b] [b, q] -> [1, b] [b, q] [q, b] [b, q] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [1, p] [p, q] ,
  [1, q] [q, q] ->= [1, 0] [0, q] [q, 0] [0, q] ,
  [1, q] [q, q] ->= [1, 1] [1, q] [q, 1] [1, q] ,
  [1, q] [q, q] ->= [1, 0] [0, p] [p, 0] [0, q] ,
  [1, q] [q, q] ->= [1, 1] [1, p] [p, 1] [1, q] ,
  [1, b] [b, p] [p, b] [b, 1] -> [1, b] [b, q] [q, b] [b, 1] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [1, p] [p, 1] ,
  [1, q] [q, 1] ->= [1, 0] [0, q] [q, 0] [0, 1] ,
  [1, q] [q, 1] ->= [1, 1] [1, q] [q, 1] [1, 1] ,
  [1, q] [q, 1] ->= [1, 0] [0, p] [p, 0] [0, 1] ,
  [1, q] [q, 1] ->= [1, 1] [1, p] [p, 1] [1, 1] ,
  [1, b] [b, p] [p, b] [b, 0] -> [1, b] [b, q] [q, b] [b, 0] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [1, p] [p, 0] ,
  [1, q] [q, 0] ->= [1, 0] [0, q] [q, 0] [0, 0] ,
  [1, q] [q, 0] ->= [1, 1] [1, q] [q, 1] [1, 0] ,
  [1, q] [q, 0] ->= [1, 0] [0, p] [p, 0] [0, 0] ,
  [1, q] [q, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] ,
  [0, b] [b, p] [p, b] [b, b] -> [0, b] [b, q] [q, b] [b, b] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [0, p] [p, b] ,
  [0, q] [q, b] ->= [0, 0] [0, q] [q, 0] [0, b] ,
  [0, q] [q, b] ->= [0, 1] [1, q] [q, 1] [1, b] ,
  [0, q] [q, b] ->= [0, 0] [0, p] [p, 0] [0, b] ,
  [0, q] [q, b] ->= [0, 1] [1, p] [p, 1] [1, b] ,
  [0, b] [b, p] [p, b] [b, p] -> [0, b] [b, q] [q, b] [b, p] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [0, p] [p, p] ,
  [0, q] [q, p] ->= [0, 0] [0, q] [q, 0] [0, p] ,
  [0, q] [q, p] ->= [0, 1] [1, q] [q, 1] [1, p] ,
  [0, q] [q, p] ->= [0, 0] [0, p] [p, 0] [0, p] ,
  [0, q] [q, p] ->= [0, 1] [1, p] [p, 1] [1, p] ,
  [0, b] [b, p] [p, b] [b, q] -> [0, b] [b, q] [q, b] [b, q] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [0, p] [p, q] ,
  [0, q] [q, q] ->= [0, 0] [0, q] [q, 0] [0, q] ,
  [0, q] [q, q] ->= [0, 1] [1, q] [q, 1] [1, q] ,
  [0, q] [q, q] ->= [0, 0] [0, p] [p, 0] [0, q] ,
  [0, q] [q, q] ->= [0, 1] [1, p] [p, 1] [1, q] ,
  [0, b] [b, p] [p, b] [b, 1] -> [0, b] [b, q] [q, b] [b, 1] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [0, p] [p, 1] ,
  [0, q] [q, 1] ->= [0, 0] [0, q] [q, 0] [0, 1] ,
  [0, q] [q, 1] ->= [0, 1] [1, q] [q, 1] [1, 1] ,
  [0, q] [q, 1] ->= [0, 0] [0, p] [p, 0] [0, 1] ,
  [0, q] [q, 1] ->= [0, 1] [1, p] [p, 1] [1, 1] ,
  [0, b] [b, p] [p, b] [b, 0] -> [0, b] [b, q] [q, b] [b, 0] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [0, p] [p, 0] ,
  [0, q] [q, 0] ->= [0, 0] [0, q] [q, 0] [0, 0] ,
  [0, q] [q, 0] ->= [0, 1] [1, q] [q, 1] [1, 0] ,
  [0, q] [q, 0] ->= [0, 0] [0, p] [p, 0] [0, 0] ,
  [0, q] [q, 0] ->= [0, 1] [1, p] [p, 1] [1, 0] }



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

[b, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, q] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[1, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 114-rule system
{ [b, b] [b, p] [p, b] [b, b] -> [b, b] [b, q] [q, b] [b, b] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [b, p] [p, b] ,
  [b, q] [q, b] ->= [b, 0] [0, q] [q, 0] [0, b] ,
  [b, q] [q, b] ->= [b, 1] [1, q] [q, 1] [1, b] ,
  [b, q] [q, b] ->= [b, 0] [0, p] [p, 0] [0, b] ,
  [b, q] [q, b] ->= [b, 1] [1, p] [p, 1] [1, b] ,
  [b, b] [b, p] [p, b] [b, p] -> [b, b] [b, q] [q, b] [b, p] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [b, p] [p, p] ,
  [b, q] [q, p] ->= [b, 0] [0, q] [q, 0] [0, p] ,
  [b, q] [q, p] ->= [b, 1] [1, q] [q, 1] [1, p] ,
  [b, q] [q, p] ->= [b, 0] [0, p] [p, 0] [0, p] ,
  [b, q] [q, p] ->= [b, 1] [1, p] [p, 1] [1, p] ,
  [b, b] [b, p] [p, b] [b, q] -> [b, b] [b, q] [q, b] [b, q] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [b, p] [p, q] ,
  [b, b] [b, p] [p, b] [b, 1] -> [b, b] [b, q] [q, b] [b, 1] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [b, p] [p, 1] ,
  [b, q] [q, 1] ->= [b, 0] [0, q] [q, 0] [0, 1] ,
  [b, q] [q, 1] ->= [b, 1] [1, q] [q, 1] [1, 1] ,
  [b, q] [q, 1] ->= [b, 0] [0, p] [p, 0] [0, 1] ,
  [b, q] [q, 1] ->= [b, 1] [1, p] [p, 1] [1, 1] ,
  [b, b] [b, p] [p, b] [b, 0] -> [b, b] [b, q] [q, b] [b, 0] ,
  [b, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [b, p] [p, 0] ,
  [b, q] [q, 0] ->= [b, 0] [0, q] [q, 0] [0, 0] ,
  [b, q] [q, 0] ->= [b, 1] [1, q] [q, 1] [1, 0] ,
  [b, q] [q, 0] ->= [b, 0] [0, p] [p, 0] [0, 0] ,
  [b, q] [q, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] ,
  [p, b] [b, p] [p, b] [b, b] -> [p, b] [b, q] [q, b] [b, b] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [p, p] [p, b] ,
  [p, q] [q, b] ->= [p, 0] [0, q] [q, 0] [0, b] ,
  [p, q] [q, b] ->= [p, 1] [1, q] [q, 1] [1, b] ,
  [p, q] [q, b] ->= [p, 0] [0, p] [p, 0] [0, b] ,
  [p, q] [q, b] ->= [p, 1] [1, p] [p, 1] [1, b] ,
  [p, b] [b, p] [p, b] [b, p] -> [p, b] [b, q] [q, b] [b, p] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [p, p] [p, p] ,
  [p, q] [q, p] ->= [p, 0] [0, q] [q, 0] [0, p] ,
  [p, q] [q, p] ->= [p, 1] [1, q] [q, 1] [1, p] ,
  [p, q] [q, p] ->= [p, 0] [0, p] [p, 0] [0, p] ,
  [p, q] [q, p] ->= [p, 1] [1, p] [p, 1] [1, p] ,
  [p, b] [b, p] [p, b] [b, q] -> [p, b] [b, q] [q, b] [b, q] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [p, p] [p, q] ,
  [p, b] [b, p] [p, b] [b, 1] -> [p, b] [b, q] [q, b] [b, 1] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [p, p] [p, 1] ,
  [p, q] [q, 1] ->= [p, 0] [0, q] [q, 0] [0, 1] ,
  [p, q] [q, 1] ->= [p, 1] [1, q] [q, 1] [1, 1] ,
  [p, q] [q, 1] ->= [p, 0] [0, p] [p, 0] [0, 1] ,
  [p, q] [q, 1] ->= [p, 1] [1, p] [p, 1] [1, 1] ,
  [p, b] [b, p] [p, b] [b, 0] -> [p, b] [b, q] [q, b] [b, 0] ,
  [p, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [p, p] [p, 0] ,
  [p, q] [q, 0] ->= [p, 0] [0, q] [q, 0] [0, 0] ,
  [p, q] [q, 0] ->= [p, 1] [1, q] [q, 1] [1, 0] ,
  [p, q] [q, 0] ->= [p, 0] [0, p] [p, 0] [0, 0] ,
  [p, q] [q, 0] ->= [p, 1] [1, p] [p, 1] [1, 0] ,
  [q, b] [b, p] [p, b] [b, b] -> [q, b] [b, q] [q, b] [b, b] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [q, p] [p, b] ,
  [q, b] [b, p] [p, b] [b, p] -> [q, b] [b, q] [q, b] [b, p] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [q, p] [p, p] ,
  [q, b] [b, p] [p, b] [b, q] -> [q, b] [b, q] [q, b] [b, q] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [q, p] [p, q] ,
  [q, b] [b, p] [p, b] [b, 1] -> [q, b] [b, q] [q, b] [b, 1] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [q, p] [p, 1] ,
  [q, b] [b, p] [p, b] [b, 0] -> [q, b] [b, q] [q, b] [b, 0] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [q, p] [p, 0] ,
  [1, b] [b, p] [p, b] [b, b] -> [1, b] [b, q] [q, b] [b, b] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [1, p] [p, b] ,
  [1, q] [q, b] ->= [1, 0] [0, q] [q, 0] [0, b] ,
  [1, q] [q, b] ->= [1, 1] [1, q] [q, 1] [1, b] ,
  [1, q] [q, b] ->= [1, 0] [0, p] [p, 0] [0, b] ,
  [1, q] [q, b] ->= [1, 1] [1, p] [p, 1] [1, b] ,
  [1, b] [b, p] [p, b] [b, p] -> [1, b] [b, q] [q, b] [b, p] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [1, p] [p, p] ,
  [1, q] [q, p] ->= [1, 0] [0, q] [q, 0] [0, p] ,
  [1, q] [q, p] ->= [1, 1] [1, q] [q, 1] [1, p] ,
  [1, q] [q, p] ->= [1, 0] [0, p] [p, 0] [0, p] ,
  [1, q] [q, p] ->= [1, 1] [1, p] [p, 1] [1, p] ,
  [1, b] [b, p] [p, b] [b, q] -> [1, b] [b, q] [q, b] [b, q] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [1, p] [p, q] ,
  [1, b] [b, p] [p, b] [b, 1] -> [1, b] [b, q] [q, b] [b, 1] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [1, p] [p, 1] ,
  [1, q] [q, 1] ->= [1, 0] [0, q] [q, 0] [0, 1] ,
  [1, q] [q, 1] ->= [1, 1] [1, q] [q, 1] [1, 1] ,
  [1, q] [q, 1] ->= [1, 0] [0, p] [p, 0] [0, 1] ,
  [1, q] [q, 1] ->= [1, 1] [1, p] [p, 1] [1, 1] ,
  [1, b] [b, p] [p, b] [b, 0] -> [1, b] [b, q] [q, b] [b, 0] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [1, p] [p, 0] ,
  [1, q] [q, 0] ->= [1, 0] [0, q] [q, 0] [0, 0] ,
  [1, q] [q, 0] ->= [1, 1] [1, q] [q, 1] [1, 0] ,
  [1, q] [q, 0] ->= [1, 0] [0, p] [p, 0] [0, 0] ,
  [1, q] [q, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] ,
  [0, b] [b, p] [p, b] [b, b] -> [0, b] [b, q] [q, b] [b, b] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [0, p] [p, b] ,
  [0, q] [q, b] ->= [0, 0] [0, q] [q, 0] [0, b] ,
  [0, q] [q, b] ->= [0, 1] [1, q] [q, 1] [1, b] ,
  [0, q] [q, b] ->= [0, 0] [0, p] [p, 0] [0, b] ,
  [0, q] [q, b] ->= [0, 1] [1, p] [p, 1] [1, b] ,
  [0, b] [b, p] [p, b] [b, p] -> [0, b] [b, q] [q, b] [b, p] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, p] ->= [0, p] [p, p] ,
  [0, q] [q, p] ->= [0, 0] [0, q] [q, 0] [0, p] ,
  [0, q] [q, p] ->= [0, 1] [1, q] [q, 1] [1, p] ,
  [0, q] [q, p] ->= [0, 0] [0, p] [p, 0] [0, p] ,
  [0, q] [q, p] ->= [0, 1] [1, p] [p, 1] [1, p] ,
  [0, b] [b, p] [p, b] [b, q] -> [0, b] [b, q] [q, b] [b, q] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [0, p] [p, q] ,
  [0, b] [b, p] [p, b] [b, 1] -> [0, b] [b, q] [q, b] [b, 1] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 1] ->= [0, p] [p, 1] ,
  [0, q] [q, 1] ->= [0, 0] [0, q] [q, 0] [0, 1] ,
  [0, q] [q, 1] ->= [0, 1] [1, q] [q, 1] [1, 1] ,
  [0, q] [q, 1] ->= [0, 0] [0, p] [p, 0] [0, 1] ,
  [0, q] [q, 1] ->= [0, 1] [1, p] [p, 1] [1, 1] ,
  [0, b] [b, p] [p, b] [b, 0] -> [0, b] [b, q] [q, b] [b, 0] ,
  [0, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [0, p] [p, 0] ,
  [0, q] [q, 0] ->= [0, 0] [0, q] [q, 0] [0, 0] ,
  [0, q] [q, 0] ->= [0, 1] [1, q] [q, 1] [1, 0] ,
  [0, q] [q, 0] ->= [0, 0] [0, p] [p, 0] [0, 0] ,
  [0, q] [q, 0] ->= [0, 1] [1, p] [p, 1] [1, 0] }


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

[b, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, p] is interpreted by
 /   \
| 1 7 |
| 0 1 |
 \   /
[p, b] is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
[b, q] is interpreted by
 /   \
| 1 8 |
| 0 1 |
 \   /
[q, b] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[b, 1] is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
[1, p] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[p, 0] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[0, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, b] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[b, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, q] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[q, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, q] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[q, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, p] is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
[p, q] is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
[1, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 42-rule system
{ [b, q] [q, p] ->= [b, 1] [1, q] [q, 1] [1, p] ,
  [b, q] [q, p] ->= [b, 1] [1, p] [p, 1] [1, p] ,
  [b, q] [q, 1] ->= [b, 1] [1, q] [q, 1] [1, 1] ,
  [b, q] [q, 1] ->= [b, 1] [1, p] [p, 1] [1, 1] ,
  [b, q] [q, 0] ->= [b, 1] [1, q] [q, 1] [1, 0] ,
  [b, q] [q, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] ,
  [p, q] [q, b] ->= [p, 0] [0, q] [q, 0] [0, b] ,
  [p, q] [q, b] ->= [p, 0] [0, p] [p, 0] [0, b] ,
  [p, q] [q, 1] ->= [p, 0] [0, q] [q, 0] [0, 1] ,
  [p, q] [q, 1] ->= [p, 0] [0, p] [p, 0] [0, 1] ,
  [p, q] [q, 0] ->= [p, 0] [0, q] [q, 0] [0, 0] ,
  [p, q] [q, 0] ->= [p, 0] [0, p] [p, 0] [0, 0] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [q, p] [p, b] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [q, p] [p, q] ,
  [q, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [q, p] [p, 0] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, b] ->= [1, p] [p, b] ,
  [1, q] [q, b] ->= [1, 0] [0, q] [q, 0] [0, b] ,
  [1, q] [q, b] ->= [1, 0] [0, p] [p, 0] [0, b] ,
  [1, q] [q, p] ->= [1, 1] [1, q] [q, 1] [1, p] ,
  [1, q] [q, p] ->= [1, 1] [1, p] [p, 1] [1, p] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, q] ->= [1, p] [p, q] ,
  [1, q] [q, 1] ->= [1, 0] [0, q] [q, 0] [0, 1] ,
  [1, q] [q, 1] ->= [1, 1] [1, q] [q, 1] [1, 1] ,
  [1, q] [q, 1] ->= [1, 0] [0, p] [p, 0] [0, 1] ,
  [1, q] [q, 1] ->= [1, 1] [1, p] [p, 1] [1, 1] ,
  [1, 1] [1, p] [p, 0] [0, 1] [1, 0] [0, 0] ->= [1, p] [p, 0] ,
  [1, q] [q, 0] ->= [1, 0] [0, q] [q, 0] [0, 0] ,
  [1, q] [q, 0] ->= [1, 1] [1, q] [q, 1] [1, 0] ,
  [1, q] [q, 0] ->= [1, 0] [0, p] [p, 0] [0, 0] ,
  [1, q] [q, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] ,
  [0, q] [q, b] ->= [0, 0] [0, q] [q, 0] [0, b] ,
  [0, q] [q, b] ->= [0, 0] [0, p] [p, 0] [0, b] ,
  [0, q] [q, p] ->= [0, 1] [1, q] [q, 1] [1, p] ,
  [0, q] [q, p] ->= [0, 1] [1, p] [p, 1] [1, p] ,
  [0, q] [q, 1] ->= [0, 0] [0, q] [q, 0] [0, 1] ,
  [0, q] [q, 1] ->= [0, 1] [1, q] [q, 1] [1, 1] ,
  [0, q] [q, 1] ->= [0, 0] [0, p] [p, 0] [0, 1] ,
  [0, q] [q, 1] ->= [0, 1] [1, p] [p, 1] [1, 1] ,
  [0, q] [q, 0] ->= [0, 0] [0, q] [q, 0] [0, 0] ,
  [0, q] [q, 0] ->= [0, 1] [1, q] [q, 1] [1, 0] ,
  [0, q] [q, 0] ->= [0, 0] [0, p] [p, 0] [0, 0] ,
  [0, q] [q, 0] ->= [0, 1] [1, p] [p, 1] [1, 0] }


The system is trivially terminating.