7.75/2.93	MAYBE
7.75/2.93	
7.75/2.93	Proof:
7.75/2.93	ConCon could not decide confluence of the system.
7.75/2.93	\cite{ALS94}, Theorem 4.1 does not apply.
7.75/2.93	This system is of type 3 or smaller.
7.75/2.93	This system is strongly deterministic.
7.75/2.93	This system is quasi-decreasing.
7.75/2.93	By \cite{A14}, Theorem 11.5.9.
7.75/2.93	This system is of type 3 or smaller.
7.75/2.93	This system is deterministic.
7.75/2.93	System R transformed to V(R) + Emb.
7.75/2.93	This system is terminating.
7.75/2.93	Call external tool:
7.75/2.93	./ttt2.sh
7.75/2.93	Input:
7.75/2.93	(VAR x)
7.75/2.93	(RULES
7.75/2.93	  even(0) -> true
7.75/2.93	  even(s(x)) -> true
7.75/2.93	  even(s(x)) -> odd(x)
7.75/2.93	  even(s(x)) -> false
7.75/2.93	  even(s(x)) -> even(x)
7.75/2.93	  odd(0) -> false
7.75/2.93	  odd(s(x)) -> true
7.75/2.93	  odd(s(x)) -> even(x)
7.75/2.93	  odd(s(x)) -> false
7.75/2.93	  odd(s(x)) -> odd(x)
7.75/2.93	  even(x) -> x
7.75/2.93	  s(x) -> x
7.75/2.93	  odd(x) -> x
7.75/2.93	)
7.75/2.93	
7.75/2.93	 Matrix Interpretation Processor: dim=3
7.75/2.93	  
7.75/2.93	  interpretation:
7.75/2.93	             [1]
7.75/2.93	   [false] = [0]
7.75/2.93	             [1],
7.75/2.93	   
7.75/2.93	               [1 0 0]  
7.75/2.93	   [odd](x0) = [0 1 0]x0
7.75/2.93	               [1 0 1]  ,
7.75/2.93	   
7.75/2.93	             [1 1 0]     [1]
7.75/2.93	   [s](x0) = [1 1 0]x0 + [0]
7.75/2.93	             [0 0 1]     [0],
7.75/2.93	   
7.75/2.93	            [0]
7.75/2.93	   [true] = [0]
7.75/2.93	            [1],
7.75/2.93	   
7.75/2.93	                [1 0 0]     [0]
7.75/2.94	   [even](x0) = [0 1 0]x0 + [0]
7.75/2.94	                [0 1 1]     [1],
7.75/2.94	   
7.75/2.94	         [1]
7.75/2.94	   [0] = [0]
7.75/2.94	         [0]
7.75/2.94	  orientation:
7.75/2.94	               [1]    [0]         
7.75/2.94	   even(0()) = [0] >= [0] = true()
7.75/2.94	               [1]    [1]         
7.75/2.94	   
7.75/2.94	                [1 1 0]    [1]    [0]         
7.75/2.94	   even(s(x)) = [1 1 0]x + [0] >= [0] = true()
7.75/2.94	                [1 1 1]    [1]    [1]         
7.75/2.94	   
7.75/2.94	                [1 1 0]    [1]    [1 0 0]          
7.75/2.94	   even(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = odd(x)
7.75/2.94	                [1 1 1]    [1]    [1 0 1]          
7.75/2.94	   
7.75/2.94	                [1 1 0]    [1]    [1]          
7.75/2.94	   even(s(x)) = [1 1 0]x + [0] >= [0] = false()
7.75/2.94	                [1 1 1]    [1]    [1]          
7.75/2.94	   
7.75/2.94	                [1 1 0]    [1]    [1 0 0]    [0]          
7.75/2.94	   even(s(x)) = [1 1 0]x + [0] >= [0 1 0]x + [0] = even(x)
7.75/2.94	                [1 1 1]    [1]    [0 1 1]    [1]          
7.75/2.94	   
7.75/2.94	              [1]    [1]          
7.75/2.94	   odd(0()) = [0] >= [0] = false()
7.75/2.94	              [1]    [1]          
7.75/2.94	   
7.75/2.94	               [1 1 0]    [1]    [0]         
7.75/2.94	   odd(s(x)) = [1 1 0]x + [0] >= [0] = true()
7.75/2.94	               [1 1 1]    [1]    [1]         
7.75/2.94	   
7.75/2.94	               [1 1 0]    [1]    [1 0 0]    [0]          
7.75/2.94	   odd(s(x)) = [1 1 0]x + [0] >= [0 1 0]x + [0] = even(x)
7.75/2.94	               [1 1 1]    [1]    [0 1 1]    [1]          
7.75/2.94	   
7.75/2.94	               [1 1 0]    [1]    [1]          
7.75/2.94	   odd(s(x)) = [1 1 0]x + [0] >= [0] = false()
7.75/2.94	               [1 1 1]    [1]    [1]          
7.75/2.94	   
7.75/2.94	               [1 1 0]    [1]    [1 0 0]          
7.75/2.94	   odd(s(x)) = [1 1 0]x + [0] >= [0 1 0]x = odd(x)
7.75/2.94	               [1 1 1]    [1]    [1 0 1]          
7.75/2.94	   
7.75/2.94	             [1 0 0]    [0]         
7.75/2.94	   even(x) = [0 1 0]x + [0] >= x = x
7.75/2.94	             [0 1 1]    [1]         
7.75/2.94	   
7.75/2.94	          [1 1 0]    [1]         
7.75/2.94	   s(x) = [1 1 0]x + [0] >= x = x
7.75/2.94	          [0 0 1]    [0]         
7.75/2.94	   
7.75/2.94	            [1 0 0]          
7.75/2.94	   odd(x) = [0 1 0]x >= x = x
7.75/2.94	            [1 0 1]          
7.75/2.94	  problem:
7.75/2.94	   even(s(x)) -> false()
7.75/2.94	   odd(0()) -> false()
7.75/2.94	   odd(s(x)) -> false()
7.75/2.94	   even(x) -> x
7.75/2.94	   odd(x) -> x
7.75/2.94	  Matrix Interpretation Processor: dim=3
7.75/2.94	   
7.75/2.94	   interpretation:
7.75/2.94	              [0]
7.75/2.94	    [false] = [0]
7.75/2.94	              [0],
7.75/2.94	    
7.75/2.94	                     [1]
7.75/2.94	    [odd](x0) = x0 + [0]
7.75/2.94	                     [0],
7.75/2.94	    
7.75/2.94	              [1 0 0]  
7.75/2.94	    [s](x0) = [0 0 0]x0
7.75/2.94	              [0 0 0]  ,
7.75/2.94	    
7.75/2.94	                      [1]
7.75/2.94	    [even](x0) = x0 + [0]
7.75/2.94	                      [0],
7.75/2.94	    
7.75/2.94	          [0]
7.75/2.94	    [0] = [0]
7.75/2.94	          [0]
7.75/2.94	   orientation:
7.75/2.94	                 [1 0 0]    [1]    [0]          
7.75/2.94	    even(s(x)) = [0 0 0]x + [0] >= [0] = false()
7.75/2.94	                 [0 0 0]    [0]    [0]          
7.75/2.94	    
7.75/2.94	               [1]    [0]          
7.75/2.94	    odd(0()) = [0] >= [0] = false()
7.75/2.94	               [0]    [0]          
7.75/2.94	    
7.75/2.94	                [1 0 0]    [1]    [0]          
7.75/2.94	    odd(s(x)) = [0 0 0]x + [0] >= [0] = false()
7.75/2.94	                [0 0 0]    [0]    [0]          
7.75/2.94	    
7.75/2.94	                  [1]         
7.75/2.94	    even(x) = x + [0] >= x = x
7.75/2.94	                  [0]         
7.75/2.94	    
7.75/2.94	                 [1]         
7.75/2.94	    odd(x) = x + [0] >= x = x
7.75/2.94	                 [0]         
7.75/2.94	   problem:
7.75/2.94	    
7.75/2.94	   Qed
7.75/2.94	This critical pair is conditional.
7.75/2.94	This critical pair has some non-trivial conditions.
7.75/2.94	ConCon could not decide whether all 4 critical pairs are joinable or not.
7.75/2.94	Overlap: (rule1: even(s(y)) -> false <= even(y) = true, rule2: even(s(z)) -> true <= odd(z) = true, pos: ε, mgu: {(y,z)})
7.75/2.94	CP: true = false <= even(z) = true, odd(z) = true
7.75/2.94	ConCon could not decide infeasibility of this critical pair.
7.75/2.94	
7.75/2.97	EOF