8.98/3.16	MAYBE
8.98/3.16	
8.98/3.16	Proof:
8.98/3.16	ConCon could not decide confluence of the system.
8.98/3.16	\cite{ALS94}, Theorem 4.1 does not apply.
8.98/3.16	This system is of type 3 or smaller.
8.98/3.16	This system is strongly deterministic.
8.98/3.16	This system is quasi-decreasing.
8.98/3.16	By \cite{A14}, Theorem 11.5.9.
8.98/3.16	This system is of type 3 or smaller.
8.98/3.16	This system is deterministic.
8.98/3.16	System R transformed to V(R) + Emb.
8.98/3.16	This system is terminating.
8.98/3.16	Call external tool:
8.98/3.16	./ttt2.sh
8.98/3.16	Input:
8.98/3.16	(VAR x)
8.98/3.16	(RULES
8.98/3.16	  e(0) -> true
8.98/3.16	  e(s(x)) -> true
8.98/3.16	  e(s(x)) -> o(x)
8.98/3.16	  e(s(x)) -> false
8.98/3.16	  e(s(x)) -> e(x)
8.98/3.16	  o(0) -> true
8.98/3.16	  o(s(x)) -> true
8.98/3.16	  o(s(x)) -> e(x)
8.98/3.16	  o(s(x)) -> false
8.98/3.16	  o(s(x)) -> o(x)
8.98/3.16	  s(x) -> x
8.98/3.16	  o(x) -> x
8.98/3.16	  e(x) -> x
8.98/3.16	)
8.98/3.16	
8.98/3.16	 Matrix Interpretation Processor: dim=3
8.98/3.16	  
8.98/3.16	  interpretation:
8.98/3.16	             [1]
8.98/3.16	   [false] = [0]
8.98/3.16	             [0],
8.98/3.16	   
8.98/3.16	             [1 0 0]  
8.98/3.16	   [o](x0) = [0 1 0]x0
8.98/3.16	             [1 0 1]  ,
8.98/3.16	   
8.98/3.16	             [1 1 0]     [1]
8.98/3.16	   [s](x0) = [1 1 0]x0 + [0]
8.98/3.16	             [0 0 1]     [0],
8.98/3.16	   
8.98/3.16	            [0]
8.98/3.16	   [true] = [0]
8.98/3.16	            [0],
8.98/3.16	   
8.98/3.16	             [1 0 0]  
8.98/3.16	   [e](x0) = [0 1 0]x0
8.98/3.16	             [0 1 1]  ,
8.98/3.16	   
8.98/3.16	         [1]
8.98/3.16	   [0] = [0]
8.98/3.16	         [0]
8.98/3.16	  orientation:
8.98/3.16	            [1]    [0]         
8.98/3.16	   e(0()) = [0] >= [0] = true()
8.98/3.16	            [0]    [0]         
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [0]         
8.98/3.16	   e(s(x)) = [1 1 0]x + [0] >= [0] = true()
8.98/3.16	             [1 1 1]    [0]    [0]         
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [1 0 0]        
8.98/3.16	   e(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = o(x)
8.98/3.16	             [1 1 1]    [0]    [1 0 1]        
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [1]          
8.98/3.16	   e(s(x)) = [1 1 0]x + [0] >= [0] = false()
8.98/3.16	             [1 1 1]    [0]    [0]          
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [1 0 0]        
8.98/3.16	   e(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = e(x)
8.98/3.16	             [1 1 1]    [0]    [0 1 1]        
8.98/3.16	   
8.98/3.16	            [1]    [0]         
8.98/3.16	   o(0()) = [0] >= [0] = true()
8.98/3.16	            [1]    [0]         
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [0]         
8.98/3.16	   o(s(x)) = [1 1 0]x + [0] >= [0] = true()
8.98/3.16	             [1 1 1]    [1]    [0]         
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [1 0 0]        
8.98/3.16	   o(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = e(x)
8.98/3.16	             [1 1 1]    [1]    [0 1 1]        
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [1]          
8.98/3.16	   o(s(x)) = [1 1 0]x + [0] >= [0] = false()
8.98/3.16	             [1 1 1]    [1]    [0]          
8.98/3.16	   
8.98/3.16	             [1 1 0]    [1]    [1 0 0]        
8.98/3.16	   o(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = o(x)
8.98/3.16	             [1 1 1]    [1]    [1 0 1]        
8.98/3.16	   
8.98/3.16	          [1 1 0]    [1]         
8.98/3.16	   s(x) = [1 1 0]x + [0] >= x = x
8.98/3.16	          [0 0 1]    [0]         
8.98/3.16	   
8.98/3.16	          [1 0 0]          
8.98/3.16	   o(x) = [0 1 0]x >= x = x
8.98/3.17	          [1 0 1]          
8.98/3.17	   
8.98/3.17	          [1 0 0]          
8.98/3.17	   e(x) = [0 1 0]x >= x = x
8.98/3.17	          [0 1 1]          
8.98/3.17	  problem:
8.98/3.17	   e(s(x)) -> false()
8.98/3.17	   o(s(x)) -> false()
8.98/3.17	   o(x) -> x
8.98/3.17	   e(x) -> x
8.98/3.17	  Matrix Interpretation Processor: dim=3
8.98/3.17	   
8.98/3.17	   interpretation:
8.98/3.17	              [0]
8.98/3.17	    [false] = [0]
8.98/3.17	              [0],
8.98/3.17	    
8.98/3.17	              [1 0 0]     [1]
8.98/3.17	    [o](x0) = [1 1 0]x0 + [0]
8.98/3.17	              [0 0 1]     [0],
8.98/3.17	    
8.98/3.17	              [1 0 0]  
8.98/3.17	    [s](x0) = [0 0 0]x0
8.98/3.17	              [0 1 0]  ,
8.98/3.17	    
8.98/3.17	              [1 0 1]     [1]
8.98/3.17	    [e](x0) = [0 1 0]x0 + [0]
8.98/3.17	              [0 0 1]     [0]
8.98/3.17	   orientation:
8.98/3.17	              [1 1 0]    [1]    [0]          
8.98/3.17	    e(s(x)) = [0 0 0]x + [0] >= [0] = false()
8.98/3.17	              [0 1 0]    [0]    [0]          
8.98/3.17	    
8.98/3.17	              [1 0 0]    [1]    [0]          
8.98/3.17	    o(s(x)) = [1 0 0]x + [0] >= [0] = false()
8.98/3.17	              [0 1 0]    [0]    [0]          
8.98/3.17	    
8.98/3.17	           [1 0 0]    [1]         
8.98/3.17	    o(x) = [1 1 0]x + [0] >= x = x
8.98/3.17	           [0 0 1]    [0]         
8.98/3.17	    
8.98/3.17	           [1 0 1]    [1]         
8.98/3.17	    e(x) = [0 1 0]x + [0] >= x = x
8.98/3.17	           [0 0 1]    [0]         
8.98/3.17	   problem:
8.98/3.17	    
8.98/3.17	   Qed
8.98/3.17	This critical pair is conditional.
8.98/3.17	This critical pair has some non-trivial conditions.
8.98/3.17	ConCon could not decide whether all 4 critical pairs are joinable or not.
8.98/3.17	Overlap: (rule1: e(s(y)) -> false <= e(y) = true, rule2: e(s(z)) -> true <= o(z) = true, pos: ε, mgu: {(y,z)})
8.98/3.17	CP: true = false <= e(z) = true, o(z) = true
8.98/3.17	ConCon could not decide infeasibility of this critical pair.
8.98/3.17	
9.16/3.20	EOF