17.98/5.24	YES
17.98/5.24	
17.98/5.24	Problem:
17.98/5.24	 strict:
17.98/5.24	  b(c(a(x1))) -> d(d(x1))
17.98/5.24	  b(x1) -> c(c(x1))
17.98/5.24	  a(a(x1)) -> a(c(b(a(x1))))
17.98/5.24	 weak:
17.98/5.24	  a(b(x1)) -> d(x1)
17.98/5.24	  d(x1) -> a(b(x1))
17.98/5.24	
17.98/5.24	Proof:
17.98/5.24	 String Reversal Processor:
17.98/5.24	  strict:
17.98/5.24	   a(c(b(x1))) -> d(d(x1))
17.98/5.24	   b(x1) -> c(c(x1))
17.98/5.24	   a(a(x1)) -> a(b(c(a(x1))))
17.98/5.24	  weak:
17.98/5.24	   b(a(x1)) -> d(x1)
17.98/5.24	   d(x1) -> b(a(x1))
17.98/5.24	  Matrix Interpretation Processor: dim=3
17.98/5.24	   
17.98/5.24	   interpretation:
17.98/5.24	              [1 0 1]     [0]
17.98/5.24	    [d](x0) = [0 0 0]x0 + [2]
17.98/5.24	              [0 0 0]     [0],
17.98/5.24	    
17.98/5.24	              [1 0 0]     [0]
17.98/5.24	    [b](x0) = [0 0 1]x0 + [2]
17.98/5.24	              [0 0 0]     [0],
17.98/5.24	    
17.98/5.24	              [1 0 0]  
17.98/5.24	    [c](x0) = [0 0 0]x0
17.98/5.24	              [0 2 0]  ,
17.98/5.24	    
17.98/5.24	              [1 0 1]     [0]
17.98/5.24	    [a](x0) = [0 0 0]x0 + [2]
17.98/5.24	              [0 0 0]     [0]
17.98/5.24	   orientation:
17.98/5.24	                  [1 0 2]     [4]    [1 0 1]     [0]           
17.98/5.24	    a(c(b(x1))) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = d(d(x1))
17.98/5.24	                  [0 0 0]     [0]    [0 0 0]     [0]           
17.98/5.24	    
17.98/5.24	            [1 0 0]     [0]    [1 0 0]             
17.98/5.24	    b(x1) = [0 0 1]x1 + [2] >= [0 0 0]x1 = c(c(x1))
17.98/5.25	            [0 0 0]     [0]    [0 0 0]             
17.98/5.25	    
17.98/5.25	               [1 0 1]     [0]    [1 0 1]     [0]                 
17.98/5.25	    a(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = a(b(c(a(x1))))
17.98/5.25	               [0 0 0]     [0]    [0 0 0]     [0]                 
17.98/5.25	    
17.98/5.25	               [1 0 1]     [0]    [1 0 1]     [0]        
17.98/5.25	    b(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = d(x1)
17.98/5.25	               [0 0 0]     [0]    [0 0 0]     [0]        
17.98/5.25	    
17.98/5.25	            [1 0 1]     [0]    [1 0 1]     [0]           
17.98/5.25	    d(x1) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = b(a(x1))
17.98/5.25	            [0 0 0]     [0]    [0 0 0]     [0]           
17.98/5.25	   problem:
17.98/5.25	    strict:
17.98/5.25	     b(x1) -> c(c(x1))
17.98/5.25	     a(a(x1)) -> a(b(c(a(x1))))
17.98/5.25	    weak:
17.98/5.25	     b(a(x1)) -> d(x1)
17.98/5.25	     d(x1) -> b(a(x1))
17.98/5.25	   String Reversal Processor:
17.98/5.25	    strict:
17.98/5.25	     b(x1) -> c(c(x1))
17.98/5.25	     a(a(x1)) -> a(c(b(a(x1))))
17.98/5.25	    weak:
17.98/5.25	     a(b(x1)) -> d(x1)
17.98/5.25	     d(x1) -> a(b(x1))
17.98/5.25	    Matrix Interpretation Processor: dim=2
17.98/5.25	     
17.98/5.25	     interpretation:
17.98/5.25	                [3 0]     [0]
17.98/5.25	      [d](x0) = [1 0]x0 + [1],
17.98/5.25	      
17.98/5.25	                [1 0]  
17.98/5.25	      [b](x0) = [1 0]x0,
17.98/5.25	      
17.98/5.25	                [1 0]  
17.98/5.25	      [c](x0) = [0 0]x0,
17.98/5.25	      
17.98/5.25	                [1 2]     [0]
17.98/5.25	      [a](x0) = [1 0]x0 + [1]
17.98/5.25	     orientation:
17.98/5.25	              [1 0]      [1 0]             
17.98/5.25	      b(x1) = [1 0]x1 >= [0 0]x1 = c(c(x1))
17.98/5.25	      
17.98/5.25	                 [3 2]     [2]    [1 2]     [0]                 
17.98/5.25	      a(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = a(c(b(a(x1))))
17.98/5.25	      
17.98/5.25	                 [3 0]     [0]    [3 0]     [0]        
17.98/5.25	      a(b(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = d(x1)
17.98/5.25	      
17.98/5.25	              [3 0]     [0]    [3 0]     [0]           
17.98/5.25	      d(x1) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a(b(x1))
17.98/5.25	     problem:
17.98/5.25	      strict:
17.98/5.25	       b(x1) -> c(c(x1))
17.98/5.25	      weak:
17.98/5.25	       a(b(x1)) -> d(x1)
17.98/5.25	       d(x1) -> a(b(x1))
17.98/5.25	     String Reversal Processor:
17.98/5.25	      strict:
17.98/5.25	       b(x1) -> c(c(x1))
17.98/5.25	      weak:
17.98/5.25	       b(a(x1)) -> d(x1)
17.98/5.25	       d(x1) -> b(a(x1))
17.98/5.25	      Arctic Interpretation Processor:
17.98/5.25	       dimension: 2
17.98/5.25	       interpretation:
17.98/5.25	                  [5  3 ]  
17.98/5.25	        [d](x0) = [-& 2 ]x0,
17.98/5.25	        
17.98/5.25	                  [1  3 ]  
17.98/5.25	        [b](x0) = [-& 2 ]x0,
17.98/5.25	        
17.98/5.25	                    
17.98/5.25	        [c](x0) = x0,
17.98/5.25	        
17.98/5.25	                  [4  0 ]  
17.98/5.25	        [a](x0) = [-& 0 ]x0
17.98/5.25	       orientation:
17.98/5.25	                [1  3 ]                   
17.98/5.25	        b(x1) = [-& 2 ]x1 >= x1 = c(c(x1))
17.98/5.25	        
17.98/5.25	                   [5  3 ]      [5  3 ]          
17.98/5.25	        b(a(x1)) = [-& 2 ]x1 >= [-& 2 ]x1 = d(x1)
17.98/5.25	        
17.98/5.25	                [5  3 ]      [5  3 ]             
17.98/5.25	        d(x1) = [-& 2 ]x1 >= [-& 2 ]x1 = b(a(x1))
17.98/5.25	       problem:
17.98/5.25	        strict:
17.98/5.25	         
17.98/5.25	        weak:
17.98/5.25	         b(a(x1)) -> d(x1)
17.98/5.25	         d(x1) -> b(a(x1))
17.98/5.25	       Qed
19.48/5.25	EOF