11.96/3.28	YES
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was reversed.
12.19/3.34	
12.19/3.34	Remains to prove termination of the 15-rule system
12.19/3.34	{ 0 r0 -> r0 0 ,
12.19/3.34	  1 r0 -> r0 1 ,
12.19/3.34	  m r0 -> r0 m ,
12.19/3.34	  0 r1 -> r1 0 ,
12.19/3.34	  1 r1 -> r1 1 ,
12.19/3.34	  m r1 -> r1 m ,
12.19/3.34	  b r0 -> b 0 qr ,
12.19/3.34	  b r1 -> b 1 qr ,
12.19/3.34	  qr 0 -> 0 qr ,
12.19/3.34	  qr 1 -> 1 qr ,
12.19/3.34	  qr m -> m ql ,
12.19/3.34	  ql 0 -> 0 ql ,
12.19/3.34	  ql 1 -> 1 ql ,
12.19/3.34	  0 ql b -> r0 b 0 ,
12.19/3.34	  1 ql b -> r1 b 1 }
12.19/3.34	
12.19/3.34	
12.19/3.34	The dependency pairs transformation was applied.
12.19/3.34	
12.19/3.34	Remains to prove termination of the 41-rule system
12.19/3.34	{ (0,true) (r0,false) -> (0,true) ,
12.19/3.34	  (1,true) (r0,false) -> (1,true) ,
12.19/3.34	  (m,true) (r0,false) -> (m,true) ,
12.19/3.34	  (0,true) (r1,false) -> (0,true) ,
12.19/3.34	  (1,true) (r1,false) -> (1,true) ,
12.19/3.34	  (m,true) (r1,false) -> (m,true) ,
12.19/3.34	  (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (qr,true) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (m,false) -> (m,true) (ql,false) ,
12.19/3.34	  (qr,true) (m,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (0,false) -> (0,true) (ql,false) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (1,true) (ql,false) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,true) (ql,false) (b,false) -> (b,true) (0,false) ,
12.19/3.34	  (0,true) (ql,false) (b,false) -> (0,true) ,
12.19/3.34	  (1,true) (ql,false) (b,false) -> (b,true) (1,false) ,
12.19/3.34	  (1,true) (ql,false) (b,false) -> (1,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 2:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 39-rule system
12.19/3.34	{ (0,true) (r0,false) -> (0,true) ,
12.19/3.34	  (1,true) (r0,false) -> (1,true) ,
12.19/3.34	  (m,true) (r0,false) -> (m,true) ,
12.19/3.34	  (0,true) (r1,false) -> (0,true) ,
12.19/3.34	  (1,true) (r1,false) -> (1,true) ,
12.19/3.34	  (m,true) (r1,false) -> (m,true) ,
12.19/3.34	  (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (qr,true) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (0,false) -> (0,true) (ql,false) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (1,true) (ql,false) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,true) (ql,false) (b,false) -> (b,true) (0,false) ,
12.19/3.34	  (0,true) (ql,false) (b,false) -> (0,true) ,
12.19/3.34	  (1,true) (ql,false) (b,false) -> (b,true) (1,false) ,
12.19/3.34	  (1,true) (ql,false) (b,false) -> (1,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 2:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 37-rule system
12.19/3.34	{ (0,true) (r0,false) -> (0,true) ,
12.19/3.34	  (1,true) (r0,false) -> (1,true) ,
12.19/3.34	  (m,true) (r0,false) -> (m,true) ,
12.19/3.34	  (0,true) (r1,false) -> (0,true) ,
12.19/3.34	  (1,true) (r1,false) -> (1,true) ,
12.19/3.34	  (m,true) (r1,false) -> (m,true) ,
12.19/3.34	  (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (qr,true) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,true) (ql,false) (b,false) -> (b,true) (0,false) ,
12.19/3.34	  (0,true) (ql,false) (b,false) -> (0,true) ,
12.19/3.34	  (1,true) (ql,false) (b,false) -> (b,true) (1,false) ,
12.19/3.34	  (1,true) (ql,false) (b,false) -> (1,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 2:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 33-rule system
12.19/3.34	{ (0,true) (r0,false) -> (0,true) ,
12.19/3.34	  (1,true) (r0,false) -> (1,true) ,
12.19/3.34	  (m,true) (r0,false) -> (m,true) ,
12.19/3.34	  (0,true) (r1,false) -> (0,true) ,
12.19/3.34	  (1,true) (r1,false) -> (1,true) ,
12.19/3.34	  (m,true) (r1,false) -> (m,true) ,
12.19/3.34	  (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (b,true) (r0,false) -> (qr,true) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 2:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 29-rule system
12.19/3.34	{ (0,true) (r0,false) -> (0,true) ,
12.19/3.34	  (1,true) (r0,false) -> (1,true) ,
12.19/3.34	  (m,true) (r0,false) -> (m,true) ,
12.19/3.34	  (0,true) (r1,false) -> (0,true) ,
12.19/3.34	  (1,true) (r1,false) -> (1,true) ,
12.19/3.34	  (m,true) (r1,false) -> (m,true) ,
12.19/3.34	  (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (0,true) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (1,true) (qr,false) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 2:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 27-rule system
12.19/3.34	{ (0,true) (r0,false) -> (0,true) ,
12.19/3.34	  (1,true) (r0,false) -> (1,true) ,
12.19/3.34	  (m,true) (r0,false) -> (m,true) ,
12.19/3.34	  (0,true) (r1,false) -> (0,true) ,
12.19/3.34	  (1,true) (r1,false) -> (1,true) ,
12.19/3.34	  (m,true) (r1,false) -> (m,true) ,
12.19/3.34	  (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 2:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 1 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /   \
12.19/3.34	| 1 0 |
12.19/3.34	| 0 1 |
12.19/3.34	 \   /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 21-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (0,false) -> (ql,true) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 1 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 20-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (ql,true) (1,false) -> (ql,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 1 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 19-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (qr,true) (0,false) -> (qr,true) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 1 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 18-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (qr,true) (1,false) -> (qr,true) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 1 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 17-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (m,false) (r1,false) ->= (r1,false) (m,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 1 |
12.19/3.34	 \     /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 1 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 16-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (b,true) (r1,false) -> (b,true) (1,false) (qr,false) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.34	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.34	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.34	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.34	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.34	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.34	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.34	
12.19/3.34	
12.19/3.34	The system was filtered by the following matrix interpretation
12.19/3.34	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.34	
12.19/3.34	(0,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(m,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(r1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	 \     /
12.19/3.34	(b,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 1 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(0,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(qr,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(qr,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(1,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 1 |
12.19/3.34	 \     /
12.19/3.34	(m,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(ql,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	 \     /
12.19/3.34	(ql,true) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	(b,false) is interpreted by
12.19/3.34	 /     \
12.19/3.34	| 1 0 0 |
12.19/3.34	| 0 1 0 |
12.19/3.34	| 0 0 0 |
12.19/3.34	 \     /
12.19/3.34	
12.19/3.34	Remains to prove termination of the 15-rule system
12.19/3.34	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.34	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.34	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.34	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.34	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.34	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.34	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.34	  (b,false) (r1,false) ->= (b,false) (1,false) (qr,false) ,
12.19/3.35	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.35	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.35	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.35	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.35	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.35	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.35	
12.19/3.35	
12.19/3.35	The system was filtered by the following matrix interpretation
12.19/3.35	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.35	
12.19/3.35	(0,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(r0,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(1,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(m,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(r1,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	 \     /
12.19/3.35	(b,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(0,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(qr,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(qr,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(1,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(m,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(ql,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	 \     /
12.19/3.35	(ql,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(b,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 1 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	
12.19/3.35	Remains to prove termination of the 14-rule system
12.19/3.35	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.35	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.35	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.35	  (m,false) (r0,false) ->= (r0,false) (m,false) ,
12.19/3.35	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.35	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.35	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.35	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.35	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.35	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.35	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.35	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.35	
12.19/3.35	
12.19/3.35	The system was filtered by the following matrix interpretation
12.19/3.35	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.35	
12.19/3.35	(0,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(r0,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 1 1 |
12.19/3.35	 \     /
12.19/3.35	(1,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(m,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(r1,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(b,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(0,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 1 1 |
12.19/3.35	 \     /
12.19/3.35	(qr,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(qr,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(1,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(m,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 1 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(ql,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(ql,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(b,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	
12.19/3.35	Remains to prove termination of the 13-rule system
12.19/3.35	{ (b,true) (r0,false) -> (b,true) (0,false) (qr,false) ,
12.19/3.35	  (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.35	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.35	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.35	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.35	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.35	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.35	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.35	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.35	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.35	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.35	
12.19/3.35	
12.19/3.35	The system was filtered by the following matrix interpretation
12.19/3.35	of type E_J with J = {1,...,2} and dimension 3:
12.19/3.35	
12.19/3.35	(0,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(r0,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	 \     /
12.19/3.35	(1,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(m,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(r1,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(b,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 1 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(0,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(qr,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(qr,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(1,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 1 |
12.19/3.35	 \     /
12.19/3.35	(m,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(ql,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	 \     /
12.19/3.35	(ql,true) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	(b,false) is interpreted by
12.19/3.35	 /     \
12.19/3.35	| 1 0 0 |
12.19/3.35	| 0 1 0 |
12.19/3.35	| 0 0 0 |
12.19/3.35	 \     /
12.19/3.35	
12.19/3.35	Remains to prove termination of the 12-rule system
12.19/3.35	{ (0,false) (r0,false) ->= (r0,false) (0,false) ,
12.19/3.35	  (1,false) (r0,false) ->= (r0,false) (1,false) ,
12.19/3.35	  (0,false) (r1,false) ->= (r1,false) (0,false) ,
12.19/3.35	  (1,false) (r1,false) ->= (r1,false) (1,false) ,
12.19/3.35	  (b,false) (r0,false) ->= (b,false) (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (0,false) ->= (0,false) (qr,false) ,
12.19/3.35	  (qr,false) (1,false) ->= (1,false) (qr,false) ,
12.19/3.35	  (qr,false) (m,false) ->= (m,false) (ql,false) ,
12.19/3.35	  (ql,false) (0,false) ->= (0,false) (ql,false) ,
12.19/3.35	  (ql,false) (1,false) ->= (1,false) (ql,false) ,
12.19/3.35	  (0,false) (ql,false) (b,false) ->= (r0,false) (b,false) (0,false) ,
12.19/3.35	  (1,false) (ql,false) (b,false) ->= (r1,false) (b,false) (1,false) }
12.19/3.35	
12.19/3.35	
12.19/3.35	The system is trivially terminating.
12.26/3.38	EOF