5.85/2.45	MAYBE
5.85/2.45	
5.85/2.45	Proof:
5.85/2.45	ConCon could not decide confluence of the system.
5.85/2.45	\cite{ALS94}, Theorem 4.1 does not apply.
5.85/2.45	This system is of type 3 or smaller.
5.85/2.45	This system is strongly deterministic.
5.85/2.45	This system is quasi-decreasing.
5.85/2.45	By \cite{A14}, Theorem 11.5.9.
5.85/2.45	This system is of type 3 or smaller.
5.85/2.45	This system is deterministic.
5.85/2.45	System R transformed to V(R) + Emb.
5.85/2.45	This system is terminating.
5.85/2.45	Call external tool:
5.85/2.45	./ttt2.sh
5.85/2.45	Input:
5.85/2.45	(VAR x)
5.85/2.45	(RULES
5.85/2.45	  s(p(x)) -> x
5.85/2.45	  p(s(x)) -> x
5.85/2.45	  pos(0) -> false
5.85/2.45	  pos(s(0)) -> true
5.85/2.45	  pos(s(x)) -> true
5.85/2.45	  pos(s(x)) -> pos(x)
5.85/2.45	  pos(p(x)) -> false
5.85/2.45	  pos(p(x)) -> pos(x)
5.85/2.45	  pos(x) -> x
5.85/2.45	  p(x) -> x
5.85/2.45	  s(x) -> x
5.85/2.45	)
5.85/2.45	
5.85/2.45	 Matrix Interpretation Processor: dim=3
5.85/2.45	  
5.85/2.45	  interpretation:
5.85/2.45	            [0]
5.85/2.45	   [true] = [0]
5.85/2.45	            [0],
5.85/2.45	   
5.85/2.45	             [0]
5.85/2.45	   [false] = [0]
5.85/2.45	             [0],
5.85/2.45	   
5.85/2.45	                    [1]
5.85/2.45	   [pos](x0) = x0 + [0]
5.85/2.45	                    [0],
5.85/2.45	   
5.85/2.45	         [0]
5.85/2.45	   [0] = [0]
5.85/2.45	         [0],
5.85/2.45	   
5.85/2.45	               
5.85/2.45	   [s](x0) = x0
5.85/2.45	               ,
5.85/2.45	   
5.85/2.45	               
5.85/2.45	   [p](x0) = x0
5.85/2.45	               
5.85/2.45	  orientation:
5.85/2.45	                       
5.85/2.45	   s(p(x)) = x >= x = x
5.85/2.45	                       
5.85/2.45	   
5.85/2.45	                       
5.85/2.45	   p(s(x)) = x >= x = x
5.85/2.45	                       
5.85/2.45	   
5.85/2.45	              [1]    [0]          
5.85/2.45	   pos(0()) = [0] >= [0] = false()
5.85/2.45	              [0]    [0]          
5.85/2.45	   
5.85/2.45	                 [1]    [0]         
5.85/2.45	   pos(s(0())) = [0] >= [0] = true()
5.85/2.45	                 [0]    [0]         
5.85/2.45	   
5.85/2.45	                   [1]    [0]         
5.85/2.45	   pos(s(x)) = x + [0] >= [0] = true()
5.85/2.45	                   [0]    [0]         
5.85/2.45	   
5.85/2.45	                   [1]        [1]         
5.85/2.45	   pos(s(x)) = x + [0] >= x + [0] = pos(x)
5.85/2.45	                   [0]        [0]         
5.85/2.45	   
5.85/2.45	                   [1]    [0]          
5.85/2.45	   pos(p(x)) = x + [0] >= [0] = false()
5.85/2.45	                   [0]    [0]          
5.85/2.45	   
5.85/2.45	                   [1]        [1]         
5.85/2.45	   pos(p(x)) = x + [0] >= x + [0] = pos(x)
5.85/2.45	                   [0]        [0]         
5.85/2.45	   
5.85/2.46	                [1]         
5.85/2.46	   pos(x) = x + [0] >= x = x
5.85/2.46	                [0]         
5.85/2.46	   
5.85/2.46	                    
5.85/2.46	   p(x) = x >= x = x
5.85/2.46	                    
5.85/2.46	   
5.85/2.46	                    
5.85/2.46	   s(x) = x >= x = x
5.85/2.46	                    
5.85/2.46	  problem:
5.85/2.46	   s(p(x)) -> x
5.85/2.46	   p(s(x)) -> x
5.85/2.46	   pos(s(x)) -> pos(x)
5.85/2.46	   pos(p(x)) -> pos(x)
5.85/2.46	   p(x) -> x
5.85/2.46	   s(x) -> x
5.85/2.46	  Matrix Interpretation Processor: dim=1
5.85/2.46	   
5.85/2.46	   interpretation:
5.85/2.46	    [pos](x0) = 4x0,
5.85/2.46	    
5.85/2.46	    [s](x0) = 4x0 + 5,
5.85/2.46	    
5.85/2.46	    [p](x0) = 5x0 + 2
5.85/2.46	   orientation:
5.85/2.46	    s(p(x)) = 20x + 13 >= x = x
5.85/2.46	    
5.85/2.46	    p(s(x)) = 20x + 27 >= x = x
5.85/2.46	    
5.85/2.46	    pos(s(x)) = 16x + 20 >= 4x = pos(x)
5.85/2.46	    
5.85/2.46	    pos(p(x)) = 20x + 8 >= 4x = pos(x)
5.85/2.46	    
5.85/2.46	    p(x) = 5x + 2 >= x = x
5.85/2.46	    
5.85/2.46	    s(x) = 4x + 5 >= x = x
5.85/2.46	   problem:
5.85/2.46	    
5.85/2.46	   Qed
5.85/2.46	Overlap: (rule1: s(p(y)) -> y, rule2: p(s(z)) -> z, pos: 1, mgu: {(y,s(z))})
5.85/2.46	CP: s(z) = s(z)
5.85/2.46	This critical pair is context-joinable.
5.85/2.46	Overlap: (rule1: p(s(y)) -> y, rule2: s(p(z)) -> z, pos: 1, mgu: {(y,p(z))})
5.85/2.46	CP: p(z) = p(z)
5.85/2.46	This critical pair is context-joinable.
5.85/2.46	Overlap: (rule1: pos(s(0)) -> true, rule2: pos(s(y)) -> true <= pos(y) = true, pos: ε, mgu: {(y,0)})
5.85/2.46	CP: true = true <= pos(0) = true
5.85/2.46	This critical pair is context-joinable.
5.85/2.46	This critical pair is conditional.
5.85/2.46	This critical pair has some non-trivial conditions.
5.85/2.46	ConCon could not decide whether all 6 critical pairs are joinable or not.
5.85/2.46	Overlap: (rule1: pos(s(y)) -> true <= pos(y) = true, rule2: s(p(z)) -> z, pos: 1, mgu: {(y,p(z))})
5.85/2.46	CP: pos(z) = true <= pos(p(z)) = true
5.85/2.46	ConCon could not decide infeasibility of this critical pair.
5.85/2.46	
5.85/2.48	EOF