0.00/0.41	YES
0.00/0.42	
0.00/0.42	
0.00/0.42	
0.00/0.42	
0.00/0.42	The system was filtered by the following matrix interpretation
0.00/0.42	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.42	
0.00/0.42	1 is interpreted by
0.00/0.42	 /     \
0.00/0.42	|  1 12 |
0.00/0.42	|  0  1 |
0.00/0.42	 \     /
0.00/0.42	4 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 8 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	3 is interpreted by
0.00/0.42	 /     \
0.00/0.42	|  1 16 |
0.00/0.42	|  0  1 |
0.00/0.42	 \     /
0.00/0.42	2 is interpreted by
0.00/0.42	 /     \
0.00/0.42	|  1 18 |
0.00/0.42	|  0  1 |
0.00/0.42	 \     /
0.00/0.42	5 is interpreted by
0.00/0.42	 /     \
0.00/0.42	|  1 17 |
0.00/0.42	|  0  1 |
0.00/0.42	 \     /
0.00/0.42	6 is interpreted by
0.00/0.42	 /     \
0.00/0.42	|  1 15 |
0.00/0.42	|  0  1 |
0.00/0.42	 \     /
0.00/0.42	
0.00/0.42	Remains to prove termination of the 7-rule system
0.00/0.42	{ 1 1 -> 4 3 ,
0.00/0.42	  1 2 -> 2 1 ,
0.00/0.42	  2 2 -> 1 1 1 ,
0.00/0.42	  3 3 -> 5 6 ,
0.00/0.42	  3 4 -> 1 1 ,
0.00/0.42	  4 4 -> 3 ,
0.00/0.42	  6 6 -> 2 1 }
0.00/0.42	
0.00/0.42	
0.00/0.42	The system was filtered by the following matrix interpretation
0.00/0.42	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.42	
0.00/0.42	1 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	4 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	3 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	2 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 2 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	5 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	6 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 2 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	
0.00/0.42	Remains to prove termination of the 4-rule system
0.00/0.42	{ 1 1 -> 4 3 ,
0.00/0.42	  1 2 -> 2 1 ,
0.00/0.42	  3 3 -> 5 6 ,
0.00/0.42	  3 4 -> 1 1 }
0.00/0.42	
0.00/0.42	
0.00/0.42	The system was filtered by the following matrix interpretation
0.00/0.42	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.42	
0.00/0.42	1 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	4 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	3 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	2 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	5 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	6 is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	
0.00/0.42	Remains to prove termination of the 3-rule system
0.00/0.42	{ 1 1 -> 4 3 ,
0.00/0.42	  1 2 -> 2 1 ,
0.00/0.42	  3 4 -> 1 1 }
0.00/0.42	
0.00/0.42	
0.00/0.42	The dependency pairs transformation was applied.
0.00/0.42	
0.00/0.42	Remains to prove termination of the 7-rule system
0.00/0.42	{ (1,true) (1,false) -> (3,true) ,
0.00/0.42	  (1,true) (2,false) -> (1,true) ,
0.00/0.42	  (3,true) (4,false) -> (1,true) (1,false) ,
0.00/0.42	  (3,true) (4,false) -> (1,true) ,
0.00/0.42	  (1,false) (1,false) ->= (4,false) (3,false) ,
0.00/0.42	  (1,false) (2,false) ->= (2,false) (1,false) ,
0.00/0.42	  (3,false) (4,false) ->= (1,false) (1,false) }
0.00/0.42	
0.00/0.42	
0.00/0.42	
0.00/0.42	
0.00/0.42	The system was filtered by the following matrix interpretation
0.00/0.42	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.42	
0.00/0.42	(1,true) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(1,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(3,true) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(2,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(4,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(3,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	
0.00/0.42	Remains to prove termination of the 6-rule system
0.00/0.42	{ (1,true) (1,false) -> (3,true) ,
0.00/0.42	  (3,true) (4,false) -> (1,true) (1,false) ,
0.00/0.42	  (3,true) (4,false) -> (1,true) ,
0.00/0.42	  (1,false) (1,false) ->= (4,false) (3,false) ,
0.00/0.42	  (1,false) (2,false) ->= (2,false) (1,false) ,
0.00/0.42	  (3,false) (4,false) ->= (1,false) (1,false) }
0.00/0.42	
0.00/0.42	
0.00/0.42	The system was filtered by the following matrix interpretation
0.00/0.42	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.42	
0.00/0.42	(1,true) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(1,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(3,true) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(2,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(4,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(3,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	
0.00/0.42	Remains to prove termination of the 4-rule system
0.00/0.42	{ (3,true) (4,false) -> (1,true) (1,false) ,
0.00/0.42	  (1,false) (1,false) ->= (4,false) (3,false) ,
0.00/0.42	  (1,false) (2,false) ->= (2,false) (1,false) ,
0.00/0.42	  (3,false) (4,false) ->= (1,false) (1,false) }
0.00/0.42	
0.00/0.42	
0.00/0.42	The system was filtered by the following matrix interpretation
0.00/0.42	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.42	
0.00/0.42	(1,true) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(1,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(3,true) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 1 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(2,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(4,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	(3,false) is interpreted by
0.00/0.42	 /   \
0.00/0.42	| 1 0 |
0.00/0.42	| 0 1 |
0.00/0.42	 \   /
0.00/0.42	
0.00/0.42	Remains to prove termination of the 3-rule system
0.00/0.42	{ (1,false) (1,false) ->= (4,false) (3,false) ,
0.00/0.42	  (1,false) (2,false) ->= (2,false) (1,false) ,
0.00/0.42	  (3,false) (4,false) ->= (1,false) (1,false) }
0.00/0.42	
0.00/0.42	
0.00/0.42	The system is trivially terminating.
0.00/0.45	EOF