21.02/5.61	YES
21.02/5.62	
21.02/5.62	Problem:
21.02/5.62	 strict:
21.02/5.62	  c(a(a(x1))) -> a(c(a(x1)))
21.02/5.62	  a(c(c(x1))) -> a(c(b(x1)))
21.02/5.62	  a(b(b(x1))) -> a(a(b(x1)))
21.02/5.62	 weak:
21.02/5.62	  a(c(c(x1))) -> c(a(b(x1)))
21.02/5.62	  a(a(b(x1))) -> c(a(b(x1)))
21.02/5.62	  a(b(b(x1))) -> a(b(c(x1)))
21.02/5.62	  a(a(a(x1))) -> c(b(a(x1)))
21.02/5.62	
21.02/5.62	Proof:
21.02/5.62	 String Reversal Processor:
21.02/5.62	  strict:
21.02/5.62	   a(a(c(x1))) -> a(c(a(x1)))
21.02/5.62	   c(c(a(x1))) -> b(c(a(x1)))
21.02/5.62	   b(b(a(x1))) -> b(a(a(x1)))
21.02/5.62	  weak:
21.02/5.62	   c(c(a(x1))) -> b(a(c(x1)))
21.02/5.62	   b(a(a(x1))) -> b(a(c(x1)))
21.02/5.62	   b(b(a(x1))) -> c(b(a(x1)))
21.02/5.62	   a(a(a(x1))) -> a(b(c(x1)))
21.02/5.62	  Matrix Interpretation Processor: dim=2
21.02/5.62	   
21.02/5.62	   interpretation:
21.02/5.62	              [1 1]     [0]
21.02/5.62	    [b](x0) = [0 0]x0 + [1],
21.02/5.62	    
21.02/5.62	              [1 0]     [1]
21.02/5.62	    [c](x0) = [0 0]x0 + [1],
21.02/5.62	    
21.02/5.62	              [1 0]     [1]
21.02/5.62	    [a](x0) = [0 0]x0 + [0]
21.02/5.62	   orientation:
21.02/5.62	                  [1 0]     [3]    [1 0]     [3]              
21.02/5.62	    a(a(c(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c(a(x1)))
21.02/5.62	    
21.02/5.62	                  [1 0]     [3]    [1 0]     [3]              
21.02/5.62	    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c(a(x1)))
21.02/5.62	    
21.02/5.62	                  [1 0]     [2]    [1 0]     [2]              
21.02/5.62	    b(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(a(x1)))
21.02/5.62	    
21.02/5.62	                  [1 0]     [3]    [1 0]     [2]              
21.02/5.62	    c(c(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
21.02/5.62	    
21.02/5.62	                  [1 0]     [2]    [1 0]     [2]              
21.02/5.62	    b(a(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
21.02/5.62	    
21.02/5.62	                  [1 0]     [2]    [1 0]     [2]              
21.02/5.62	    b(b(a(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = c(b(a(x1)))
21.02/5.62	    
21.02/5.62	                  [1 0]     [3]    [1 0]     [3]              
21.02/5.62	    a(a(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b(c(x1)))
21.02/5.62	   problem:
21.02/5.62	    strict:
21.02/5.62	     a(a(c(x1))) -> a(c(a(x1)))
21.02/5.62	     c(c(a(x1))) -> b(c(a(x1)))
21.02/5.62	     b(b(a(x1))) -> b(a(a(x1)))
21.02/5.62	    weak:
21.02/5.62	     b(a(a(x1))) -> b(a(c(x1)))
21.02/5.62	     b(b(a(x1))) -> c(b(a(x1)))
21.02/5.62	     a(a(a(x1))) -> a(b(c(x1)))
21.02/5.62	   Bounds Processor:
21.02/5.62	    bound: 1
21.02/5.62	    enrichment: match-rt
21.02/5.62	    automaton:
21.02/5.62	     final states: {4}
21.02/5.62	     transitions:
21.02/5.62	      a1(17) -> 18*
21.02/5.62	      a1(33) -> 34*
21.02/5.62	      c1(49) -> 50*
21.02/5.62	      c1(18) -> 19*
21.02/5.62	      b1(19) -> 20*
21.02/5.62	      a0(4) -> 4*
21.02/5.62	      c0(4) -> 4*
21.02/5.62	      b0(4) -> 4*
21.02/5.62	      4 -> 49,17
21.02/5.62	      19 -> 33*
21.02/5.62	      20 -> 50,4
21.02/5.62	      34 -> 18*
21.02/5.62	      50 -> 19*
21.02/5.62	    problem:
21.02/5.62	     strict:
21.02/5.62	      a(a(c(x1))) -> a(c(a(x1)))
21.02/5.62	      b(b(a(x1))) -> b(a(a(x1)))
21.02/5.62	     weak:
21.02/5.62	      b(a(a(x1))) -> b(a(c(x1)))
21.02/5.62	      b(b(a(x1))) -> c(b(a(x1)))
21.02/5.62	      a(a(a(x1))) -> a(b(c(x1)))
21.02/5.62	    Arctic Interpretation Processor:
21.02/5.62	     dimension: 1
21.02/5.62	     interpretation:
21.02/5.62	      [b](x0) = 1x0,
21.02/5.62	      
21.02/5.62	      [c](x0) = x0,
21.02/5.62	      
21.02/5.62	      [a](x0) = 1x0
21.02/5.62	     orientation:
21.02/5.62	      a(a(c(x1))) = 2x1 >= 2x1 = a(c(a(x1)))
21.02/5.62	      
21.02/5.62	      b(b(a(x1))) = 3x1 >= 3x1 = b(a(a(x1)))
21.02/5.62	      
21.02/5.62	      b(a(a(x1))) = 3x1 >= 2x1 = b(a(c(x1)))
21.02/5.62	      
21.02/5.62	      b(b(a(x1))) = 3x1 >= 2x1 = c(b(a(x1)))
21.02/5.62	      
21.02/5.62	      a(a(a(x1))) = 3x1 >= 2x1 = a(b(c(x1)))
21.02/5.62	     problem:
21.02/5.62	      strict:
21.02/5.62	       a(a(c(x1))) -> a(c(a(x1)))
21.02/5.62	       b(b(a(x1))) -> b(a(a(x1)))
21.02/5.62	      weak:
21.02/5.62	       
21.02/5.62	     Arctic Interpretation Processor:
21.02/5.62	      dimension: 1
21.02/5.62	      interpretation:
21.02/5.62	       [b](x0) = 6x0,
21.02/5.62	       
21.02/5.62	       [c](x0) = 1x0,
21.02/5.62	       
21.02/5.62	       [a](x0) = 3x0
21.02/5.62	      orientation:
21.02/5.62	       a(a(c(x1))) = 7x1 >= 7x1 = a(c(a(x1)))
21.02/5.62	       
21.02/5.62	       b(b(a(x1))) = 15x1 >= 12x1 = b(a(a(x1)))
21.02/5.62	      problem:
21.02/5.62	       strict:
21.02/5.62	        a(a(c(x1))) -> a(c(a(x1)))
21.02/5.62	       weak:
21.02/5.62	        
21.02/5.62	      String Reversal Processor:
21.02/5.62	       strict:
21.02/5.62	        c(a(a(x1))) -> a(c(a(x1)))
21.02/5.62	       weak:
21.02/5.62	        
21.02/5.62	       Matrix Interpretation Processor: dim=2
21.02/5.62	        
21.02/5.62	        interpretation:
21.02/5.62	                   [2 1]     [1]
21.02/5.62	         [c](x0) = [2 1]x0 + [0],
21.02/5.62	         
21.02/5.62	                        [0]
21.02/5.62	         [a](x0) = x0 + [1]
21.02/5.62	        orientation:
21.02/5.62	                       [2 1]     [3]    [2 1]     [2]              
21.02/5.62	         c(a(a(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [2] = a(c(a(x1)))
21.02/5.62	        problem:
21.02/5.62	         strict:
21.02/5.62	          
21.02/5.62	         weak:
21.02/5.62	          
21.02/5.62	        Qed
21.02/5.63	EOF