/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 4:

b is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
q is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
p is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

Remains to prove termination of the 5-rule system
{ b q b -> b p b ,
  1 p 1 ->= q ,
  0 q 0 ->= q ,
  1 q 1 ->= q ,
  p ->= 1 p 1 0 1 }


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 125-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 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, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 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, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, b] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[b, 0] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[0, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, b] 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, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 120-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, b] ->= [b, q] [q, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, p] [p, p] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, p] [p, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, b] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 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, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 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, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 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 |
 \   /
[0, b] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[1, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 116-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, b] ->= [b, q] [q, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, p] [p, p] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, p] [p, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, p] [p, b] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, p] [p, b] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, p] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [0, 1] [1, p] [p, 1] [1, 0] [0, 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, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 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, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 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 |
 \   /
[0, b] 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, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, p] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

Remains to prove termination of the 107-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, b] ->= [b, q] [q, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, p] [p, p] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, p] [p, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, p] [p, p] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, p] [p, b] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, p] [p, p] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [p, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, p] [p, p] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 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] }


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

Remains to prove termination of the 99-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, b] ->= [b, q] [q, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, p] [p, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 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] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 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] }


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

Remains to prove termination of the 93-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, b] ->= [b, q] [q, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, p] [p, 0] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, p] [p, 0] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 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, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, p] [p, 0] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 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, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, 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, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 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 |
 \   /
[0, b] 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, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, q] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[q, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, p] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[1, 1] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[0, 0] is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
[p, 0] is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

Remains to prove termination of the 88-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, p] [p, 1] [1, b] ->= [b, q] [q, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 87-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, p] [p, 1] [1, p] ->= [b, q] [q, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 86-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, p] [p, 1] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

Remains to prove termination of the 85-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, p] [p, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 84-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, p] [p, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 83-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, p] [p, 1] [1, 0] ->= [p, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 82-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, p] [p, b] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

Remains to prove termination of the 81-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, p] [p, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 80-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, p] [p, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 79-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, p] [p, 1] [1, 0] ->= [0, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 78-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 77-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, p] [p, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 76-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, p] [p, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 75-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, p] [p, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 74-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, p] [p, 1] [1, p] ->= [1, q] [q, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 73-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 1] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 72-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, p] [p, b] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

Remains to prove termination of the 71-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, p] [p, q] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

Remains to prove termination of the 70-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, p] [p, 1] [1, p] ->= [q, q] [q, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 69-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, p] [p, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 68-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, p] [p, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 67-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, p] [p, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 66-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 1] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 65-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, 1] [1, q] [q, 1] [1, b] ->= [b, q] [q, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, q] [q, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, 1] [1, q] [q, 1] [1, p] ->= [b, q] [q, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, q] [q, 1] [1, 1] ->= [b, q] [q, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [b, 1] [1, q] [q, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


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

[b, b] 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, q] 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 |
 \                 /
[q, b] 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, p] 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 |
 \                 /
[p, b] 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, 1] 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 |
 \                 /
[1, p] 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 1 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 |
 \                 /
[p, 1] 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 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 |
 \                 /
[1, b] 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, 0] 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 |
 \                 /
[0, q] 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 1 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
 \                 /
[q, 0] 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 1 |
| 0 0 0 0 0 0 0 0 0 |
 \                 /
[0, b] 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 |
 \                 /
[1, q] 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 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
 \                 /
[q, 1] 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 1 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 |
 \                 /
[1, 0] 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 1 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 0 |
| 0 0 0 0 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] 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 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 1 0 0 0 0 |
 \                 /
[q, q] 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 |
 \                 /
[p, q] 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 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 |
 \                 /
[q, p] 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 2 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, p] 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 |
 \                 /
[p, p] 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 |
 \                 /
[1, 1] is interpreted by
 /                 \
| 1 0 0 0 0 0 0 0 0 |
| 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 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] 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 |
 \                 /
[p, 0] 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 60-rule system
{ [b, b] [b, q] [q, b] [b, b] -> [b, b] [b, p] [p, b] [b, b] ,
  [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 59-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, b] [b, q] [q, b] [b, 0] -> [b, b] [b, p] [p, b] [b, 0] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 58-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, b] [b, q] [q, b] [b, b] -> [0, b] [b, p] [p, b] [b, b] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 57-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, b] [b, q] [q, b] [b, 0] -> [0, b] [b, p] [p, b] [b, 0] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 56-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, b] [b, q] [q, b] [b, q] -> [b, b] [b, p] [p, b] [b, q] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, b] [b, q] [q, b] [b, p] -> [b, b] [b, p] [p, b] [b, p] ,
  [b, b] [b, q] [q, b] [b, 1] -> [b, b] [b, p] [p, b] [b, 1] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 53-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, b] [b, q] [q, b] [b, q] -> [0, b] [b, p] [p, b] [b, q] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, b] [b, q] [q, b] [b, p] -> [0, b] [b, p] [p, b] [b, p] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, b] [b, q] [q, b] [b, 1] -> [0, b] [b, p] [p, b] [b, 1] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 50-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, b] [b, q] [q, b] [b, b] -> [q, b] [b, p] [p, b] [b, b] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, b] [b, q] [q, b] [b, b] -> [p, b] [b, p] [p, b] [b, b] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, b] [b, q] [q, b] [b, b] -> [1, b] [b, p] [p, b] [b, b] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 47-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, b] [b, q] [q, b] [b, 0] -> [q, b] [b, p] [p, b] [b, 0] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, b] [b, q] [q, b] [b, 0] -> [p, b] [b, p] [p, b] [b, 0] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, b] [b, q] [q, b] [b, 0] -> [1, b] [b, p] [p, b] [b, 0] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 44-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, b] [b, q] [q, b] [b, q] -> [q, b] [b, p] [p, b] [b, q] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, b] [b, q] [q, b] [b, p] -> [q, b] [b, p] [p, b] [b, p] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [q, b] [b, q] [q, b] [b, 1] -> [q, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, b] [b, q] [q, b] [b, q] -> [p, b] [b, p] [p, b] [b, q] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, b] [b, q] [q, b] [b, p] -> [p, b] [b, p] [p, b] [b, p] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, b] [b, q] [q, b] [b, 1] -> [p, b] [b, p] [p, b] [b, 1] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, b] [b, q] [q, b] [b, q] -> [1, b] [b, p] [p, b] [b, q] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, b] [b, q] [q, b] [b, p] -> [1, b] [b, p] [p, b] [b, p] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [1, b] [b, q] [q, b] [b, 1] -> [1, b] [b, p] [p, b] [b, 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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

Remains to prove termination of the 35-rule system
{ [b, p] [p, b] ->= [b, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, b] ,
  [b, 1] [1, p] [p, 1] [1, q] ->= [b, q] [q, q] ,
  [b, 1] [1, p] [p, 1] [1, 0] ->= [b, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, b] ->= [q, q] [q, b] ,
  [q, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [q, 1] [1, q] [q, 1] [1, p] ->= [q, q] [q, p] ,
  [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, p] [p, 1] ->= [q, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [q, 1] [1, p] [p, 1] [1, 0] ->= [q, q] [q, 0] ,
  [q, 1] [1, q] [q, 1] [1, 0] ->= [q, q] [q, 0] ,
  [p, 1] [1, q] [q, 1] [1, b] ->= [p, q] [q, b] ,
  [p, 1] [1, q] [q, 1] [1, q] ->= [p, q] [q, q] ,
  [p, 1] [1, q] [q, 1] [1, p] ->= [p, q] [q, p] ,
  [p, 1] [1, q] [q, 1] [1, 1] ->= [p, q] [q, 1] ,
  [p, 1] [1, q] [q, 1] [1, 0] ->= [p, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, b] ->= [1, q] [q, b] ,
  [1, 1] [1, p] [p, 1] [1, 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, p] [p, q] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, q] ,
  [1, 1] [1, q] [q, 1] [1, p] ->= [1, q] [q, p] ,
  [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, p] [p, 1] ->= [1, 1] [1, p] [p, 1] [1, 0] [0, 1] [1, 1] ,
  [1, 1] [1, p] [p, 1] [1, 0] ->= [1, q] [q, 0] ,
  [1, 1] [1, q] [q, 1] [1, 0] ->= [1, q] [q, 0] ,
  [0, 1] [1, q] [q, 1] [1, b] ->= [0, q] [q, b] ,
  [0, 1] [1, q] [q, 1] [1, q] ->= [0, q] [q, q] ,
  [0, 1] [1, q] [q, 1] [1, p] ->= [0, q] [q, p] ,
  [0, 1] [1, q] [q, 1] [1, 1] ->= [0, q] [q, 1] ,
  [0, 1] [1, q] [q, 1] [1, 0] ->= [0, q] [q, 0] }


The system is trivially terminating.