12.12/4.74	MAYBE
12.12/4.74	
12.12/4.74	Proof:
12.12/4.74	ConCon could not decide confluence of the system.
12.12/4.75	\cite{ALS94}, Theorem 4.1 does not apply.
12.12/4.75	This system is of type 3 or smaller.
12.12/4.75	This system is strongly deterministic.
12.12/4.75	This system is quasi-decreasing.
12.12/4.75	By \cite{A14}, Theorem 11.5.9.
12.12/4.75	This system is of type 3 or smaller.
12.12/4.75	This system is deterministic.
12.12/4.75	System R transformed to V(R) + Emb.
12.12/4.75	This system is terminating.
12.12/4.75	Call external tool:
12.12/4.75	./ttt2.sh -s COMP[30] -ext trs -
12.12/4.75	Input:
12.12/4.75	(VAR x)
12.12/4.75	(RULES
12.12/4.75	  e(0) -> true
12.12/4.75	  e(s(x)) -> true
12.12/4.75	  e(s(x)) -> o(x)
12.12/4.75	  e(s(x)) -> false
12.12/4.75	  e(s(x)) -> e(x)
12.12/4.75	  o(0) -> false
12.12/4.75	  o(s(x)) -> true
12.12/4.75	  o(s(x)) -> e(x)
12.12/4.75	  o(s(x)) -> false
12.12/4.75	  o(s(x)) -> o(x)
12.12/4.75	  s(x) -> x
12.12/4.75	  o(x) -> x
12.12/4.75	  e(x) -> x
12.12/4.75	)
12.12/4.75	
12.12/4.75	 Matrix Interpretation Processor: dim=3
12.12/4.75	  
12.12/4.75	  interpretation:
12.12/4.75	               
12.12/4.75	   [o](x0) = x0
12.12/4.75	               ,
12.12/4.75	   
12.12/4.75	               
12.12/4.75	   [e](x0) = x0
12.12/4.75	               ,
12.12/4.75	   
12.12/4.75	                  [1]
12.12/4.75	   [s](x0) = x0 + [0]
12.12/4.75	                  [0],
12.12/4.75	   
12.12/4.75	             [0]
12.12/4.75	   [false] = [0]
12.12/4.75	             [0],
12.12/4.75	   
12.12/4.75	         [1]
12.12/4.75	   [0] = [0]
12.12/4.75	         [0],
12.12/4.75	   
12.12/4.75	            [0]
12.12/4.75	   [true] = [0]
12.12/4.75	            [0]
12.12/4.75	  orientation:
12.12/4.75	            [1]    [0]         
12.12/4.75	   e(0()) = [0] >= [0] = true()
12.12/4.75	            [0]    [0]         
12.12/4.75	   
12.12/4.75	                 [1]    [0]         
12.12/4.75	   e(s(x)) = x + [0] >= [0] = true()
12.12/4.75	                 [0]    [0]         
12.12/4.75	   
12.12/4.75	                 [1]            
12.12/4.75	   e(s(x)) = x + [0] >= x = o(x)
12.12/4.75	                 [0]            
12.12/4.75	   
12.12/4.75	                 [1]    [0]          
12.12/4.75	   e(s(x)) = x + [0] >= [0] = false()
12.12/4.75	                 [0]    [0]          
12.12/4.75	   
12.12/4.75	                 [1]            
12.12/4.75	   e(s(x)) = x + [0] >= x = e(x)
12.12/4.75	                 [0]            
12.12/4.75	   
12.12/4.75	            [1]    [0]          
12.12/4.75	   o(0()) = [0] >= [0] = false()
12.12/4.75	            [0]    [0]          
12.12/4.75	   
12.12/4.75	                 [1]    [0]         
12.12/4.75	   o(s(x)) = x + [0] >= [0] = true()
12.12/4.75	                 [0]    [0]         
12.12/4.75	   
12.12/4.75	                 [1]            
12.12/4.75	   o(s(x)) = x + [0] >= x = e(x)
12.12/4.75	                 [0]            
12.12/4.75	   
12.12/4.75	                 [1]    [0]          
12.12/4.75	   o(s(x)) = x + [0] >= [0] = false()
12.12/4.75	                 [0]    [0]          
12.12/4.75	   
12.12/4.75	                 [1]            
12.12/4.75	   o(s(x)) = x + [0] >= x = o(x)
12.12/4.75	                 [0]            
12.12/4.75	   
12.12/4.75	              [1]         
12.12/4.75	   s(x) = x + [0] >= x = x
12.12/4.75	              [0]         
12.12/4.75	   
12.12/4.75	                    
12.12/4.75	   o(x) = x >= x = x
12.12/4.75	                    
12.12/4.75	   
12.12/4.75	                    
12.12/4.75	   e(x) = x >= x = x
12.12/4.75	                    
12.12/4.75	  problem:
12.12/4.75	   o(x) -> x
12.12/4.75	   e(x) -> x
12.12/4.75	  Matrix Interpretation Processor: dim=3
12.12/4.75	   
12.12/4.75	   interpretation:
12.12/4.75	                
12.12/4.75	    [o](x0) = x0
12.12/4.75	                ,
12.12/4.75	    
12.12/4.75	                   [1]
12.12/4.75	    [e](x0) = x0 + [0]
12.12/4.75	                   [0]
12.12/4.75	   orientation:
12.12/4.75	                     
12.12/4.75	    o(x) = x >= x = x
12.12/4.75	                     
12.12/4.75	    
12.12/4.75	               [1]         
12.12/4.75	    e(x) = x + [0] >= x = x
12.12/4.75	               [0]         
12.12/4.75	   problem:
12.12/4.75	    o(x) -> x
12.12/4.75	   Matrix Interpretation Processor: dim=3
12.12/4.75	    
12.12/4.75	    interpretation:
12.12/4.75	                    [1]
12.12/4.75	     [o](x0) = x0 + [0]
12.12/4.75	                    [0]
12.12/4.75	    orientation:
12.12/4.75	                [1]         
12.12/4.75	     o(x) = x + [0] >= x = x
12.12/4.75	                [0]         
12.12/4.75	    problem:
12.12/4.75	     
12.12/4.75	    Qed
12.12/4.75	This critical pair is conditional.
12.12/4.75	This critical pair has some non-trivial conditions.
12.12/4.75	ConCon could not decide whether all 4 critical pairs are joinable or not.
12.12/4.75	Overlap: (rule1: e(s(y)) -> false <= e(y) = true, rule2: e(s(z)) -> true <= o(z) = true, pos: ε, mgu: {(y,z)})
12.12/4.75	CP: true = false <= e(z) = true, o(z) = true
12.12/4.75	ConCon could not decide infeasibility of this critical pair.
12.12/4.75	maedmax: MAYBE
12.12/4.75	
12.24/4.77	EOF