4.46/1.77	YES
4.46/1.77	
4.46/1.77	Proof:
4.46/1.77	This system is confluent.
4.46/1.77	By \cite{ALS94}, Theorem 4.1.
4.46/1.77	This system is of type 3 or smaller.
4.46/1.77	This system is strongly deterministic.
4.46/1.77	This system is quasi-decreasing.
4.46/1.77	By \cite{A14}, Theorem 11.5.9.
4.46/1.77	This system is of type 3 or smaller.
4.46/1.77	This system is deterministic.
4.46/1.77	System R transformed to V(R) + Emb.
4.46/1.77	This system is terminating.
4.46/1.77	Call external tool:
4.46/1.77	./ttt2.sh
4.46/1.77	Input:
4.46/1.77	  f(x', x'') -> g(x')
4.46/1.77	  f(x', x'') -> x''
4.46/1.77	  f(x', x'') -> x'
4.46/1.77	  f(y', h(y'')) -> g(y')
4.46/1.77	  f(y', h(y'')) -> y''
4.46/1.77	  f(y', h(y'')) -> y'
4.46/1.77	  h(x) -> x
4.46/1.77	  g(x) -> x
4.46/1.77	  f(x, y) -> x
4.46/1.77	  f(x, y) -> y
4.46/1.77	
4.46/1.77	 Matrix Interpretation Processor: dim=3
4.46/1.77	  
4.46/1.77	  interpretation:
4.46/1.77	               
4.46/1.77	   [h](x0) = x0
4.46/1.77	               ,
4.46/1.77	   
4.46/1.77	               
4.46/1.77	   [g](x0) = x0
4.46/1.77	               ,
4.46/1.77	   
4.46/1.77	                           [1]
4.46/1.77	   [f](x0, x1) = x0 + x1 + [0]
4.46/1.77	                           [0]
4.46/1.77	  orientation:
4.46/1.77	                          [1]              
4.46/1.77	   f(x',x'') = x' + x'' + [0] >= x' = g(x')
4.46/1.77	                          [0]              
4.46/1.77	   
4.46/1.77	                          [1]             
4.46/1.77	   f(x',x'') = x' + x'' + [0] >= x'' = x''
4.46/1.77	                          [0]             
4.46/1.77	   
4.46/1.77	                          [1]           
4.46/1.77	   f(x',x'') = x' + x'' + [0] >= x' = x'
4.46/1.77	                          [0]           
4.46/1.77	   
4.46/1.77	                             [1]              
4.46/1.77	   f(y',h(y'')) = y' + y'' + [0] >= y' = g(y')
4.46/1.77	                             [0]              
4.46/1.77	   
4.46/1.77	                             [1]             
4.46/1.77	   f(y',h(y'')) = y' + y'' + [0] >= y'' = y''
4.46/1.77	                             [0]             
4.46/1.77	   
4.46/1.77	                             [1]           
4.46/1.77	   f(y',h(y'')) = y' + y'' + [0] >= y' = y'
4.46/1.77	                             [0]           
4.46/1.77	   
4.46/1.77	                    
4.46/1.77	   h(x) = x >= x = x
4.46/1.77	                    
4.46/1.77	   
4.46/1.77	                    
4.46/1.77	   g(x) = x >= x = x
4.46/1.77	                    
4.46/1.77	   
4.46/1.77	                    [1]         
4.46/1.77	   f(x,y) = x + y + [0] >= x = x
4.46/1.77	                    [0]         
4.46/1.77	   
4.46/1.77	                    [1]         
4.46/1.77	   f(x,y) = x + y + [0] >= y = y
4.46/1.77	                    [0]         
4.46/1.77	  problem:
4.46/1.77	   h(x) -> x
4.46/1.77	   g(x) -> x
4.46/1.77	  Matrix Interpretation Processor: dim=3
4.46/1.77	   
4.46/1.77	   interpretation:
4.46/1.77	                
4.46/1.77	    [h](x0) = x0
4.46/1.77	                ,
4.46/1.77	    
4.46/1.77	                   [1]
4.46/1.77	    [g](x0) = x0 + [0]
4.46/1.77	                   [0]
4.46/1.77	   orientation:
4.46/1.77	                     
4.46/1.77	    h(x) = x >= x = x
4.46/1.77	                     
4.46/1.77	    
4.46/1.77	               [1]         
4.46/1.77	    g(x) = x + [0] >= x = x
4.46/1.77	               [0]         
4.46/1.77	   problem:
4.46/1.77	    h(x) -> x
4.46/1.77	   Matrix Interpretation Processor: dim=3
4.46/1.77	    
4.46/1.77	    interpretation:
4.94/1.82	                    [1]
4.94/1.82	     [h](x0) = x0 + [0]
4.94/1.82	                    [0]
4.94/1.82	    orientation:
4.94/1.82	                [1]         
4.94/1.82	     h(x) = x + [0] >= x = x
4.94/1.82	                [0]         
4.94/1.82	    problem:
4.94/1.82	     
4.94/1.82	    Qed
4.94/1.82	All 2 critical pairs are joinable.
4.94/1.82	Overlap: (rule1: f(z, h(x')) -> g(x) <= z = x, x' = x, rule2: f(y', z') -> g(y) <= y' = y, z' = y, pos: ε, mgu: {(y',z), (z',h(x'))})
4.94/1.82	CP: g(y) = g(x) <= z = x, x' = x, z = y, h(x') = y
4.94/1.82	This critical pair is infeasible.
4.94/1.82	This critical pair is conditional.
4.94/1.82	This critical pair has some non-trivial conditions.
4.94/1.82	Call external tool:
4.94/1.82	./waldmeister
4.94/1.82	Input:
4.94/1.82	  f(x', x'') -> g(x) <= x' = x, x'' = x
4.94/1.82	  f(y', h(y'')) -> g(y) <= y' = y, y'' = y
4.94/1.82	
4.94/1.82	By Waldmeister.
4.94/1.82	Overlap: (rule1: f(z, y') -> g(y) <= z = y, y' = y, rule2: f(x', h(z')) -> g(x) <= x' = x, z' = x, pos: ε, mgu: {(x',z), (y',h(z'))})
4.94/1.82	CP: g(x) = g(y) <= z = y, h(z') = y, z = x, z' = x
4.94/1.82	This critical pair is infeasible.
4.94/1.82	This critical pair is conditional.
4.94/1.82	This critical pair has some non-trivial conditions.
4.94/1.82	Call external tool:
4.94/1.82	./waldmeister
4.94/1.82	Input:
4.94/1.82	  f(x', x'') -> g(x) <= x' = x, x'' = x
4.94/1.82	  f(y', h(y'')) -> g(y) <= y' = y, y'' = y
4.94/1.82	
4.94/1.82	By Waldmeister.
4.94/1.82	
4.97/1.87	EOF