22.54/6.06	YES
22.54/6.07	
22.54/6.07	Problem:
22.54/6.07	 strict:
22.54/6.07	  top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
22.54/6.07	  top(left(car(x,car(old(),y)),z)) -> top(right(car(old(),y),z))
22.54/6.07	  top(right(x,car(y,car(old(),z)))) -> top(left(x,car(old(),z)))
22.54/6.07	  top(right(car(old(),x),car(y,z))) -> top(left(car(old(),x),z))
22.54/6.07	  top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
22.54/6.07	  top(right(car(old(),x),bot())) -> top(left(car(old(),x),bot()))
22.54/6.07	 weak:
22.54/6.07	  top(left(car(x,y),z)) -> top(left(y,z))
22.54/6.07	  top(right(x,car(y,z))) -> top(right(x,z))
22.54/6.07	  bot() -> car(new(),bot())
22.54/6.07	
22.54/6.07	Proof:
22.54/6.07	 Matrix Interpretation Processor: dim=2
22.54/6.07	  
22.54/6.07	  interpretation:
22.54/6.07	           [0]
22.54/6.07	   [new] = [0],
22.54/6.07	   
22.54/6.07	           [0]
22.54/6.07	   [bot] = [0],
22.54/6.07	   
22.54/6.07	                     [1 0]     [1 0]  
22.54/6.07	   [right](x0, x1) = [0 0]x0 + [0 0]x1,
22.54/6.07	   
22.54/6.07	               [1 0]  
22.54/6.07	   [top](x0) = [1 0]x0,
22.54/6.07	   
22.54/6.07	                    [1 0]     [1 0]  
22.54/6.07	   [left](x0, x1) = [0 0]x0 + [0 0]x1,
22.54/6.07	   
22.54/6.07	           [0]
22.54/6.07	   [old] = [1],
22.54/6.07	   
22.54/6.07	                   [1 0]     [1 1]  
22.54/6.07	   [car](x0, x1) = [0 2]x0 + [0 0]x1
22.54/6.07	  orientation:
22.54/6.07	                                      [1 0]    [1 1]    [1 1]     [1 0]    [1 1]                              
22.54/6.07	   top(left(car(x,y),car(old(),z))) = [1 0]x + [1 1]y + [1 1]z >= [1 0]y + [1 1]z = top(right(y,car(old(),z)))
22.54/6.07	   
22.54/6.07	                                      [1 0]    [1 1]    [1 0]    [2]    [1 1]    [1 0]                              
22.54/6.07	   top(left(car(x,car(old(),y)),z)) = [1 0]x + [1 1]y + [1 0]z + [2] >= [1 1]y + [1 0]z = top(right(car(old(),y),z))
22.54/6.07	   
22.54/6.07	                                       [1 0]    [1 0]    [1 1]    [2]    [1 0]    [1 1]                             
22.54/6.07	   top(right(x,car(y,car(old(),z)))) = [1 0]x + [1 0]y + [1 1]z + [2] >= [1 0]x + [1 1]z = top(left(x,car(old(),z)))
22.54/6.07	   
22.54/6.07	                                       [1 1]    [1 0]    [1 1]     [1 1]    [1 0]                             
22.54/6.07	   top(right(car(old(),x),car(y,z))) = [1 1]x + [1 0]y + [1 1]z >= [1 1]x + [1 0]z = top(left(car(old(),x),z))
22.54/6.07	   
22.54/6.07	                                   [1 1]     [1 1]                                  
22.54/6.07	   top(left(bot(),car(old(),x))) = [1 1]x >= [1 1]x = top(right(bot(),car(old(),x)))
22.54/6.07	   
22.54/6.07	                                    [1 1]     [1 1]                                 
22.54/6.07	   top(right(car(old(),x),bot())) = [1 1]x >= [1 1]x = top(left(car(old(),x),bot()))
22.54/6.07	   
22.54/6.07	                           [1 0]    [1 1]    [1 0]     [1 0]    [1 0]                  
22.54/6.07	   top(left(car(x,y),z)) = [1 0]x + [1 1]y + [1 0]z >= [1 0]y + [1 0]z = top(left(y,z))
22.54/6.07	   
22.54/6.07	                            [1 0]    [1 0]    [1 1]     [1 0]    [1 0]                   
22.54/6.07	   top(right(x,car(y,z))) = [1 0]x + [1 0]y + [1 1]z >= [1 0]x + [1 0]z = top(right(x,z))
22.54/6.07	   
22.54/6.07	           [0]    [0]                   
22.54/6.07	   bot() = [0] >= [0] = car(new(),bot())
22.54/6.07	  problem:
22.54/6.07	   strict:
22.54/6.07	    top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
22.54/6.07	    top(right(car(old(),x),car(y,z))) -> top(left(car(old(),x),z))
22.54/6.07	    top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
22.54/6.07	    top(right(car(old(),x),bot())) -> top(left(car(old(),x),bot()))
22.54/6.07	   weak:
22.54/6.07	    top(left(car(x,y),z)) -> top(left(y,z))
22.54/6.07	    top(right(x,car(y,z))) -> top(right(x,z))
22.54/6.07	    bot() -> car(new(),bot())
22.54/6.07	  Matrix Interpretation Processor: dim=2
22.54/6.07	   
22.54/6.07	   interpretation:
22.54/6.07	            [0]
22.54/6.07	    [new] = [0],
22.54/6.07	    
22.54/6.07	            [0]
22.54/6.07	    [bot] = [0],
22.54/6.07	    
22.54/6.07	                      [1 0]     [3 0]  
22.54/6.07	    [right](x0, x1) = [1 0]x0 + [0 0]x1,
22.54/6.07	    
22.54/6.07	                [1 2]  
22.54/6.07	    [top](x0) = [0 3]x0,
22.54/6.07	    
22.54/6.07	                          [2 1]     [1]
22.54/6.07	    [left](x0, x1) = x0 + [0 0]x1 + [0],
22.54/6.07	    
22.54/6.07	            [1]
22.54/6.07	    [old] = [0],
22.54/6.07	    
22.54/6.07	                    [1 0]     [1 1]  
22.54/6.07	    [car](x0, x1) = [0 0]x0 + [1 1]x1
22.54/6.07	   orientation:
22.54/6.07	                                       [1 0]    [3 3]    [3 3]    [3]    [3 0]    [3 3]    [3]                             
22.54/6.07	    top(left(car(x,y),car(old(),z))) = [0 0]x + [3 3]y + [0 0]z + [0] >= [3 0]y + [0 0]z + [0] = top(right(y,car(old(),z)))
22.54/6.07	    
22.54/6.07	                                        [3 3]    [3 0]    [3 3]    [3]    [3 3]    [2 1]    [2]                            
22.54/6.07	    top(right(car(old(),x),car(y,z))) = [3 3]x + [0 0]y + [0 0]z + [3] >= [3 3]x + [0 0]z + [0] = top(left(car(old(),x),z))
22.54/6.07	    
22.54/6.07	                                    [3 3]    [3]    [3 3]    [3]                                 
22.54/6.07	    top(left(bot(),car(old(),x))) = [0 0]x + [0] >= [0 0]x + [0] = top(right(bot(),car(old(),x)))
22.54/6.07	    
22.54/6.07	                                     [3 3]    [3]    [3 3]    [2]                                
22.54/6.07	    top(right(car(old(),x),bot())) = [3 3]x + [3] >= [3 3]x + [0] = top(left(car(old(),x),bot()))
22.54/6.07	    
22.54/6.07	                            [1 0]    [3 3]    [2 1]    [1]    [1 2]    [2 1]    [1]                 
22.54/6.07	    top(left(car(x,y),z)) = [0 0]x + [3 3]y + [0 0]z + [0] >= [0 3]y + [0 0]z + [0] = top(left(y,z))
22.54/6.07	    
22.54/6.07	                             [3 0]    [3 0]    [3 3]     [3 0]    [3 0]                   
22.54/6.07	    top(right(x,car(y,z))) = [3 0]x + [0 0]y + [0 0]z >= [3 0]x + [0 0]z = top(right(x,z))
22.54/6.07	    
22.54/6.07	            [0]    [0]                   
22.54/6.07	    bot() = [0] >= [0] = car(new(),bot())
22.54/6.07	   problem:
22.54/6.07	    strict:
22.54/6.07	     top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
22.54/6.07	     top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
22.54/6.07	    weak:
22.54/6.07	     top(left(car(x,y),z)) -> top(left(y,z))
22.54/6.07	     top(right(x,car(y,z))) -> top(right(x,z))
22.54/6.07	     bot() -> car(new(),bot())
22.54/6.07	   Matrix Interpretation Processor: dim=2
22.54/6.07	    
22.54/6.07	    interpretation:
22.54/6.07	             [0]
22.54/6.07	     [new] = [0],
22.54/6.07	     
22.54/6.07	             [1]
22.54/6.07	     [bot] = [0],
22.54/6.07	     
22.54/6.07	                       [1 0]       
22.54/6.07	     [right](x0, x1) = [0 0]x0 + x1,
22.54/6.07	     
22.54/6.07	                 [1 0]  
22.54/6.07	     [top](x0) = [0 0]x0,
22.54/6.07	     
22.54/6.07	                      [2 0]     [1 0]  
22.54/6.07	     [left](x0, x1) = [0 0]x0 + [0 0]x1,
22.54/6.07	     
22.54/6.07	             [0]
22.54/6.07	     [old] = [1],
22.54/6.07	     
22.54/6.07	                          [1 0]  
22.54/6.07	     [car](x0, x1) = x0 + [0 0]x1
22.54/6.07	    orientation:
22.54/6.07	                                        [2 0]    [2 0]    [1 0]     [1 0]    [1 0]                              
22.54/6.07	     top(left(car(x,y),car(old(),z))) = [0 0]x + [0 0]y + [0 0]z >= [0 0]y + [0 0]z = top(right(y,car(old(),z)))
22.54/6.07	     
22.54/6.07	                                     [1 0]    [2]    [1 0]    [1]                                 
22.54/6.07	     top(left(bot(),car(old(),x))) = [0 0]x + [0] >= [0 0]x + [0] = top(right(bot(),car(old(),x)))
22.54/6.07	     
22.54/6.07	                             [2 0]    [2 0]    [1 0]     [2 0]    [1 0]                  
22.54/6.07	     top(left(car(x,y),z)) = [0 0]x + [0 0]y + [0 0]z >= [0 0]y + [0 0]z = top(left(y,z))
22.54/6.07	     
22.54/6.07	                              [1 0]    [1 0]    [1 0]     [1 0]    [1 0]                   
22.54/6.07	     top(right(x,car(y,z))) = [0 0]x + [0 0]y + [0 0]z >= [0 0]x + [0 0]z = top(right(x,z))
22.54/6.07	     
22.54/6.07	             [1]    [1]                   
22.54/6.07	     bot() = [0] >= [0] = car(new(),bot())
22.54/6.07	    problem:
22.54/6.07	     strict:
22.54/6.07	      top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
22.54/6.07	     weak:
22.54/6.07	      top(left(car(x,y),z)) -> top(left(y,z))
22.54/6.07	      top(right(x,car(y,z))) -> top(right(x,z))
22.54/6.07	      bot() -> car(new(),bot())
22.54/6.07	    Bounds Processor:
22.54/6.07	     bound: 1
22.54/6.07	     enrichment: match-rt
22.54/6.07	     automaton:
22.54/6.07	      final states: {8}
22.54/6.07	      transitions:
22.54/6.07	       top1(14) -> 8*
22.54/6.07	       right1(8,13) -> 14*
22.54/6.07	       right1(8,15) -> 14*
22.54/6.07	       right1(15,13) -> 14*
22.54/6.07	       right1(15,15) -> 14*
22.54/6.07	       right1(8,8) -> 14*
22.54/6.07	       right1(15,8) -> 14*
22.54/6.07	       car1(16,15) -> 15,8
22.54/6.07	       car1(12,8) -> 13*
22.54/6.07	       old1() -> 12*
22.54/6.07	       new1() -> 16*
22.54/6.07	       bot1() -> 15*
22.54/6.07	       left1(15,8) -> 14*
22.54/6.07	       top0(8) -> 8*
22.54/6.07	       left0(8,8) -> 8*
22.54/6.07	       car0(8,8) -> 8*
22.54/6.07	       old0() -> 8*
22.54/6.07	       right0(8,8) -> 8*
22.54/6.07	       bot0() -> 8*
22.54/6.07	       new0() -> 8*
22.54/6.07	     problem:
22.54/6.07	      strict:
22.54/6.07	       
22.54/6.07	      weak:
22.54/6.07	       top(left(car(x,y),z)) -> top(left(y,z))
22.54/6.07	       top(right(x,car(y,z))) -> top(right(x,z))
22.54/6.07	       bot() -> car(new(),bot())
22.54/6.07	     Qed
22.60/6.08	EOF