7.77/2.99	MAYBE
7.77/2.99	
7.77/2.99	Proof:
7.77/2.99	ConCon could not decide confluence of the system.
7.77/2.99	\cite{ALS94}, Theorem 4.1 does not apply.
7.77/2.99	This system is of type 3 or smaller.
7.77/2.99	This system is strongly deterministic.
7.77/2.99	This system is quasi-decreasing.
7.77/2.99	By \cite{A14}, Theorem 11.5.9.
7.77/2.99	This system is of type 3 or smaller.
7.77/2.99	This system is deterministic.
7.77/2.99	System R transformed to V(R) + Emb.
7.77/2.99	This system is terminating.
7.77/2.99	Call external tool:
7.77/2.99	./ttt2.sh
7.77/2.99	Input:
7.77/2.99	(VAR x)
7.77/2.99	(RULES
7.77/2.99	  even(0) -> true
7.77/2.99	  even(s(x)) -> true
7.77/2.99	  even(s(x)) -> odd(x)
7.77/2.99	  even(s(x)) -> false
7.77/2.99	  even(s(x)) -> even(x)
7.77/2.99	  odd(0) -> false
7.77/2.99	  odd(s(x)) -> true
7.77/2.99	  odd(s(x)) -> even(x)
7.77/2.99	  odd(s(x)) -> false
7.77/2.99	  odd(s(x)) -> odd(x)
7.77/2.99	  even(x) -> x
7.77/2.99	  s(x) -> x
7.77/2.99	  odd(x) -> x
7.77/2.99	)
7.77/2.99	
7.77/2.99	 Matrix Interpretation Processor: dim=3
7.77/2.99	  
7.77/2.99	  interpretation:
7.77/2.99	             [1]
7.77/2.99	   [false] = [0]
7.77/2.99	             [1],
7.77/2.99	   
7.77/2.99	               [1 0 0]  
7.77/2.99	   [odd](x0) = [0 1 0]x0
7.77/2.99	               [1 0 1]  ,
7.77/2.99	   
7.77/2.99	             [1 1 0]     [1]
7.77/2.99	   [s](x0) = [1 1 0]x0 + [0]
7.77/2.99	             [0 0 1]     [0],
7.77/2.99	   
7.77/2.99	            [0]
7.77/2.99	   [true] = [0]
7.77/2.99	            [1],
7.77/2.99	   
7.77/2.99	                [1 0 0]     [0]
7.77/2.99	   [even](x0) = [0 1 0]x0 + [0]
7.77/2.99	                [0 1 1]     [1],
7.77/2.99	   
7.77/2.99	         [1]
7.77/2.99	   [0] = [0]
7.77/2.99	         [0]
7.77/2.99	  orientation:
7.77/2.99	               [1]    [0]         
7.77/2.99	   even(0()) = [0] >= [0] = true()
7.77/2.99	               [1]    [1]         
8.02/3.00	   
8.02/3.00	                [1 1 0]    [1]    [0]         
8.02/3.00	   even(s(x)) = [1 1 0]x + [0] >= [0] = true()
8.02/3.00	                [1 1 1]    [1]    [1]         
8.02/3.00	   
8.02/3.00	                [1 1 0]    [1]    [1 0 0]          
8.02/3.00	   even(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = odd(x)
8.02/3.00	                [1 1 1]    [1]    [1 0 1]          
8.02/3.00	   
8.02/3.00	                [1 1 0]    [1]    [1]          
8.02/3.00	   even(s(x)) = [1 1 0]x + [0] >= [0] = false()
8.02/3.00	                [1 1 1]    [1]    [1]          
8.02/3.00	   
8.02/3.00	                [1 1 0]    [1]    [1 0 0]    [0]          
8.02/3.00	   even(s(x)) = [1 1 0]x + [0] >= [0 1 0]x + [0] = even(x)
8.02/3.00	                [1 1 1]    [1]    [0 1 1]    [1]          
8.02/3.00	   
8.02/3.00	              [1]    [1]          
8.02/3.00	   odd(0()) = [0] >= [0] = false()
8.02/3.00	              [1]    [1]          
8.02/3.00	   
8.02/3.00	               [1 1 0]    [1]    [0]         
8.02/3.00	   odd(s(x)) = [1 1 0]x + [0] >= [0] = true()
8.02/3.00	               [1 1 1]    [1]    [1]         
8.02/3.00	   
8.02/3.00	               [1 1 0]    [1]    [1 0 0]    [0]          
8.02/3.00	   odd(s(x)) = [1 1 0]x + [0] >= [0 1 0]x + [0] = even(x)
8.02/3.00	               [1 1 1]    [1]    [0 1 1]    [1]          
8.02/3.00	   
8.02/3.00	               [1 1 0]    [1]    [1]          
8.02/3.00	   odd(s(x)) = [1 1 0]x + [0] >= [0] = false()
8.02/3.00	               [1 1 1]    [1]    [1]          
8.02/3.00	   
8.02/3.00	               [1 1 0]    [1]    [1 0 0]          
8.02/3.00	   odd(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = odd(x)
8.02/3.00	               [1 1 1]    [1]    [1 0 1]          
8.02/3.00	   
8.02/3.00	             [1 0 0]    [0]         
8.02/3.00	   even(x) = [0 1 0]x + [0] >= x = x
8.02/3.00	             [0 1 1]    [1]         
8.02/3.00	   
8.02/3.00	          [1 1 0]    [1]         
8.02/3.00	   s(x) = [1 1 0]x + [0] >= x = x
8.02/3.00	          [0 0 1]    [0]         
8.02/3.00	   
8.02/3.00	            [1 0 0]          
8.02/3.00	   odd(x) = [0 1 0]x >= x = x
8.02/3.00	            [1 0 1]          
8.02/3.00	  problem:
8.02/3.00	   even(s(x)) -> false()
8.02/3.00	   odd(0()) -> false()
8.02/3.00	   odd(s(x)) -> false()
8.02/3.00	   even(x) -> x
8.02/3.00	   odd(x) -> x
8.02/3.00	  Matrix Interpretation Processor: dim=3
8.02/3.00	   
8.02/3.00	   interpretation:
8.02/3.00	              [0]
8.02/3.00	    [false] = [0]
8.02/3.00	              [0],
8.02/3.00	    
8.02/3.00	                     [1]
8.02/3.00	    [odd](x0) = x0 + [0]
8.02/3.00	                     [0],
8.02/3.00	    
8.02/3.00	              [1 0 0]  
8.02/3.00	    [s](x0) = [0 0 0]x0
8.02/3.00	              [0 0 0]  ,
8.02/3.00	    
8.02/3.00	                      [1]
8.02/3.00	    [even](x0) = x0 + [0]
8.02/3.00	                      [0],
8.02/3.00	    
8.02/3.00	          [0]
8.02/3.00	    [0] = [0]
8.02/3.00	          [0]
8.02/3.00	   orientation:
8.02/3.00	                 [1 0 0]    [1]    [0]          
8.02/3.00	    even(s(x)) = [0 0 0]x + [0] >= [0] = false()
8.02/3.00	                 [0 0 0]    [0]    [0]          
8.02/3.00	    
8.02/3.00	               [1]    [0]          
8.02/3.00	    odd(0()) = [0] >= [0] = false()
8.02/3.00	               [0]    [0]          
8.02/3.00	    
8.02/3.00	                [1 0 0]    [1]    [0]          
8.02/3.00	    odd(s(x)) = [0 0 0]x + [0] >= [0] = false()
8.02/3.00	                [0 0 0]    [0]    [0]          
8.02/3.00	    
8.02/3.00	                  [1]         
8.02/3.00	    even(x) = x + [0] >= x = x
8.02/3.00	                  [0]         
8.02/3.00	    
8.02/3.00	                 [1]         
8.02/3.00	    odd(x) = x + [0] >= x = x
8.02/3.00	                 [0]         
8.02/3.00	   problem:
8.02/3.00	    
8.02/3.00	   Qed
8.02/3.00	This critical pair is conditional.
8.02/3.00	This critical pair has some non-trivial conditions.
8.02/3.00	ConCon could not decide whether all 4 critical pairs are joinable or not.
8.02/3.00	Overlap: (rule1: even(s(y)) -> false <= even(y) = true, rule2: even(s(z)) -> true <= odd(z) = true, pos: ε, mgu: {(y,z)})
8.02/3.00	CP: true = false <= even(z) = true, odd(z) = true
8.02/3.00	ConCon could not decide infeasibility of this critical pair.
8.02/3.00	
8.02/3.04	EOF