3.41/1.45	YES
3.41/1.45	
3.41/1.45	Proof:
3.41/1.45	This system is confluent.
3.41/1.45	By \cite{ALS94}, Theorem 4.1.
3.41/1.45	This system is of type 3 or smaller.
3.41/1.45	This system is strongly deterministic.
3.41/1.45	This system is quasi-decreasing.
3.41/1.45	By \cite{A14}, Theorem 11.5.9.
3.41/1.45	This system is of type 3 or smaller.
3.41/1.45	This system is deterministic.
3.41/1.45	System R transformed to V(R) + Emb.
3.41/1.45	This system is terminating.
3.41/1.45	Call external tool:
3.41/1.45	./ttt2.sh
3.41/1.45	Input:
3.41/1.45	  pos(s(0)) -> true
3.41/1.45	  pos(0) -> false
3.41/1.45	  pos(s(x)) -> true
3.41/1.45	  pos(s(x)) -> pos(x)
3.41/1.45	  pos(p(x)) -> false
3.41/1.45	  pos(p(x)) -> pos(x)
3.41/1.45	  pos(x) -> x
3.41/1.45	  p(x) -> x
3.41/1.45	  s(x) -> x
3.41/1.45	
3.41/1.45	 Matrix Interpretation Processor: dim=3
3.41/1.45	  
3.41/1.45	  interpretation:
3.41/1.45	               
3.41/1.45	   [p](x0) = x0
3.41/1.45	               ,
3.41/1.45	   
3.41/1.45	             [0]
3.41/1.45	   [false] = [0]
3.41/1.45	             [0],
3.41/1.46	   
3.41/1.46	            [0]
3.41/1.46	   [true] = [0]
3.41/1.46	            [0],
3.41/1.46	   
3.41/1.46	                    [1]
3.41/1.46	   [pos](x0) = x0 + [0]
3.41/1.46	                    [0],
3.41/1.46	   
3.41/1.46	               
3.41/1.46	   [s](x0) = x0
3.41/1.46	               ,
3.41/1.46	   
3.41/1.46	         [0]
3.41/1.46	   [0] = [0]
3.41/1.46	         [0]
3.41/1.46	  orientation:
3.41/1.46	                 [1]    [0]         
3.41/1.46	   pos(s(0())) = [0] >= [0] = true()
3.41/1.46	                 [0]    [0]         
3.41/1.46	   
3.41/1.46	              [1]    [0]          
3.41/1.46	   pos(0()) = [0] >= [0] = false()
3.41/1.46	              [0]    [0]          
3.41/1.46	   
3.41/1.46	                   [1]    [0]         
3.41/1.46	   pos(s(x)) = x + [0] >= [0] = true()
3.41/1.46	                   [0]    [0]         
3.41/1.46	   
3.41/1.46	                   [1]        [1]         
3.41/1.46	   pos(s(x)) = x + [0] >= x + [0] = pos(x)
3.41/1.46	                   [0]        [0]         
3.41/1.46	   
3.41/1.46	                   [1]    [0]          
3.41/1.46	   pos(p(x)) = x + [0] >= [0] = false()
3.41/1.46	                   [0]    [0]          
3.41/1.46	   
3.41/1.46	                   [1]        [1]         
3.41/1.46	   pos(p(x)) = x + [0] >= x + [0] = pos(x)
3.41/1.46	                   [0]        [0]         
3.41/1.46	   
3.41/1.46	                [1]         
3.41/1.46	   pos(x) = x + [0] >= x = x
3.41/1.46	                [0]         
3.41/1.46	   
3.41/1.46	                    
3.41/1.46	   p(x) = x >= x = x
3.41/1.46	                    
3.41/1.46	   
3.41/1.46	                    
3.41/1.46	   s(x) = x >= x = x
3.41/1.46	                    
3.41/1.46	  problem:
3.41/1.46	   pos(s(x)) -> pos(x)
3.41/1.46	   pos(p(x)) -> pos(x)
3.41/1.46	   p(x) -> x
3.41/1.46	   s(x) -> x
3.41/1.46	  Matrix Interpretation Processor: dim=3
3.41/1.46	   
3.41/1.46	   interpretation:
3.41/1.46	                   [1]
3.41/1.46	    [p](x0) = x0 + [0]
3.41/1.46	                   [0],
3.41/1.46	    
3.41/1.46	                [1 0 0]     [0]
3.41/1.46	    [pos](x0) = [0 0 0]x0 + [0]
3.41/1.46	                [0 0 0]     [1],
3.41/1.46	    
3.41/1.46	                   [1]
3.41/1.46	    [s](x0) = x0 + [0]
3.41/1.46	                   [0]
3.41/1.46	   orientation:
3.41/1.46	                [1 0 0]    [1]    [1 0 0]    [0]         
3.41/1.46	    pos(s(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = pos(x)
3.41/1.46	                [0 0 0]    [1]    [0 0 0]    [1]         
3.41/1.46	    
3.41/1.46	                [1 0 0]    [1]    [1 0 0]    [0]         
3.41/1.46	    pos(p(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = pos(x)
3.41/1.46	                [0 0 0]    [1]    [0 0 0]    [1]         
3.41/1.46	    
3.41/1.46	               [1]         
3.41/1.46	    p(x) = x + [0] >= x = x
3.41/1.46	               [0]         
3.41/1.46	    
3.41/1.46	               [1]         
3.41/1.46	    s(x) = x + [0] >= x = x
3.41/1.46	               [0]         
3.41/1.46	   problem:
3.41/1.46	    
3.41/1.46	   Qed
3.41/1.46	All 2 critical pairs are joinable.
3.41/1.46	Overlap: (rule1: pos(s(y)) -> true <= pos(y) = true, rule2: pos(s(0)) -> true, pos: ε, mgu: {(y,0)})
3.41/1.46	CP: true = true <= pos(0) = true
3.41/1.46	This critical pair is context-joinable.
3.41/1.46	Overlap: (rule1: pos(s(0)) -> true, rule2: pos(s(y)) -> true <= pos(y) = true, pos: ε, mgu: {(y,0)})
3.41/1.46	CP: true = true <= pos(0) = true
3.41/1.46	This critical pair is context-joinable.
3.41/1.46	
3.60/1.49	EOF