0.00/0.50	YES
0.00/0.52	
0.00/0.52	
0.00/0.52	
0.00/0.52	
0.00/0.52	The system was filtered by the following matrix interpretation
0.00/0.52	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.52	
0.00/0.52	0 is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 0 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	* is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 1 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	1 is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 0 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	# is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 1 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	$ is interpreted by
0.00/0.52	 /   \
0.00/0.52	| 1 0 |
0.00/0.52	| 0 1 |
0.00/0.52	 \   /
0.00/0.52	
0.00/0.52	Remains to prove termination of the 5-rule system
0.00/0.52	{ 0 * -> * 1 ,
0.00/0.52	  1 * -> 0 # ,
0.00/0.52	  # 0 -> 0 # ,
0.00/0.52	  # 1 -> 1 # ,
0.00/0.52	  # $ -> * $ }
0.00/0.52	
0.00/0.52	
0.00/0.52	The dependency pairs transformation was applied.
0.00/0.52	
0.00/0.52	Remains to prove termination of the 12-rule system
0.00/0.52	{ (0,true) (*,false) -> (1,true) ,
0.00/0.52	  (1,true) (*,false) -> (0,true) (#,false) ,
0.00/0.52	  (1,true) (*,false) -> (#,true) ,
0.00/0.52	  (#,true) (0,false) -> (0,true) (#,false) ,
0.00/0.52	  (#,true) (0,false) -> (#,true) ,
0.00/0.52	  (#,true) (1,false) -> (1,true) (#,false) ,
0.00/0.52	  (#,true) (1,false) -> (#,true) ,
0.00/0.52	  (0,false) (*,false) ->= (*,false) (1,false) ,
0.00/0.52	  (1,false) (*,false) ->= (0,false) (#,false) ,
0.00/0.52	  (#,false) (0,false) ->= (0,false) (#,false) ,
0.00/0.52	  (#,false) (1,false) ->= (1,false) (#,false) ,
0.00/0.53	  (#,false) ($,false) ->= (*,false) ($,false) }
0.00/0.53	
0.00/0.53	
0.00/0.53	
0.00/0.53	
0.00/0.53	The system was filtered by the following matrix interpretation
0.00/0.53	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.53	
0.00/0.53	(0,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(*,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(1,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(#,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(#,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(0,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 1 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(1,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 1 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	($,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	
0.00/0.53	Remains to prove termination of the 8-rule system
0.00/0.53	{ (0,true) (*,false) -> (1,true) ,
0.00/0.53	  (1,true) (*,false) -> (0,true) (#,false) ,
0.00/0.53	  (1,true) (*,false) -> (#,true) ,
0.00/0.53	  (0,false) (*,false) ->= (*,false) (1,false) ,
0.00/0.53	  (1,false) (*,false) ->= (0,false) (#,false) ,
0.00/0.53	  (#,false) (0,false) ->= (0,false) (#,false) ,
0.00/0.53	  (#,false) (1,false) ->= (1,false) (#,false) ,
0.00/0.53	  (#,false) ($,false) ->= (*,false) ($,false) }
0.00/0.53	
0.00/0.53	
0.00/0.53	The system was filtered by the following matrix interpretation
0.00/0.53	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.53	
0.00/0.53	(0,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(*,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 1 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(1,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(#,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 1 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(#,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(0,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(1,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	($,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	
0.00/0.53	Remains to prove termination of the 6-rule system
0.00/0.53	{ (1,true) (*,false) -> (0,true) (#,false) ,
0.00/0.53	  (0,false) (*,false) ->= (*,false) (1,false) ,
0.00/0.53	  (1,false) (*,false) ->= (0,false) (#,false) ,
0.00/0.53	  (#,false) (0,false) ->= (0,false) (#,false) ,
0.00/0.53	  (#,false) (1,false) ->= (1,false) (#,false) ,
0.00/0.53	  (#,false) ($,false) ->= (*,false) ($,false) }
0.00/0.53	
0.00/0.53	
0.00/0.53	The system was filtered by the following matrix interpretation
0.00/0.53	of type E_J with J = {1,...,2} and dimension 2:
0.00/0.53	
0.00/0.53	(0,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(*,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(1,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 1 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(#,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(#,true) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(0,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	(1,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	($,false) is interpreted by
0.00/0.53	 /   \
0.00/0.53	| 1 0 |
0.00/0.53	| 0 1 |
0.00/0.53	 \   /
0.00/0.53	
0.00/0.53	Remains to prove termination of the 5-rule system
0.00/0.53	{ (0,false) (*,false) ->= (*,false) (1,false) ,
0.00/0.53	  (1,false) (*,false) ->= (0,false) (#,false) ,
0.00/0.53	  (#,false) (0,false) ->= (0,false) (#,false) ,
0.00/0.53	  (#,false) (1,false) ->= (1,false) (#,false) ,
0.00/0.53	  (#,false) ($,false) ->= (*,false) ($,false) }
0.00/0.53	
0.00/0.53	
0.00/0.53	The system is trivially terminating.
0.00/0.55	EOF