20.58/5.55	YES
20.58/5.56	
20.58/5.56	Problem:
20.58/5.56	 strict:
20.58/5.56	  a(b(a(x1))) -> b(c(c(x1)))
20.58/5.56	  b(a(c(x1))) -> a(a(c(x1)))
20.58/5.56	  a(b(a(x1))) -> a(c(c(x1)))
20.58/5.56	  b(b(a(x1))) -> a(b(a(x1)))
20.58/5.56	 weak:
20.58/5.56	  a(a(c(x1))) -> a(b(c(x1)))
20.58/5.56	  a(c(c(x1))) -> c(b(a(x1)))
20.58/5.56	  b(c(c(x1))) -> c(c(a(x1)))
20.58/5.56	
20.58/5.56	Proof:
20.58/5.56	 String Reversal Processor:
20.58/5.56	  strict:
20.58/5.56	   a(b(a(x1))) -> c(c(b(x1)))
20.58/5.56	   c(a(b(x1))) -> c(a(a(x1)))
20.58/5.56	   a(b(a(x1))) -> c(c(a(x1)))
20.58/5.56	   a(b(b(x1))) -> a(b(a(x1)))
20.58/5.56	  weak:
20.58/5.56	   c(a(a(x1))) -> c(b(a(x1)))
20.58/5.56	   c(c(a(x1))) -> a(b(c(x1)))
20.58/5.56	   c(c(b(x1))) -> a(c(c(x1)))
20.58/5.56	  Matrix Interpretation Processor: dim=2
20.58/5.56	   
20.58/5.56	   interpretation:
20.58/5.56	              [1 1]  
20.58/5.56	    [c](x0) = [1 0]x0,
20.58/5.56	    
20.58/5.56	              [1 1]     [0]
20.58/5.56	    [b](x0) = [1 0]x0 + [1],
20.58/5.56	    
20.58/5.56	              [1 1]     [0]
20.58/5.56	    [a](x0) = [1 0]x0 + [1]
20.58/5.56	   orientation:
20.58/5.56	                  [3 2]     [2]    [3 2]     [1]              
20.58/5.56	    a(b(a(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [1] = c(c(b(x1)))
20.58/5.56	    
20.58/5.56	                  [3 2]     [2]    [3 2]     [2]              
20.58/5.56	    c(a(b(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = c(a(a(x1)))
20.58/5.56	    
20.58/5.56	                  [3 2]     [2]    [3 2]     [1]              
20.58/5.56	    a(b(a(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [1] = c(c(a(x1)))
20.58/5.56	    
20.58/5.56	                  [3 2]     [2]    [3 2]     [2]              
20.58/5.56	    a(b(b(x1))) = [2 1]x1 + [2] >= [2 1]x1 + [2] = a(b(a(x1)))
20.58/5.56	    
20.58/5.56	                  [3 2]     [2]    [3 2]     [2]              
20.58/5.56	    c(a(a(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = c(b(a(x1)))
20.58/5.56	    
20.58/5.56	                  [3 2]     [1]    [3 2]     [1]              
20.58/5.56	    c(c(a(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = a(b(c(x1)))
20.58/5.56	    
20.58/5.56	                  [3 2]     [1]    [3 2]     [0]              
20.58/5.56	    c(c(b(x1))) = [2 1]x1 + [1] >= [2 1]x1 + [1] = a(c(c(x1)))
20.58/5.56	   problem:
20.58/5.56	    strict:
20.58/5.56	     c(a(b(x1))) -> c(a(a(x1)))
20.58/5.56	     a(b(b(x1))) -> a(b(a(x1)))
20.58/5.56	    weak:
20.58/5.56	     c(a(a(x1))) -> c(b(a(x1)))
20.58/5.56	     c(c(a(x1))) -> a(b(c(x1)))
20.58/5.56	   String Reversal Processor:
20.58/5.56	    strict:
20.58/5.56	     b(a(c(x1))) -> a(a(c(x1)))
20.58/5.56	     b(b(a(x1))) -> a(b(a(x1)))
20.58/5.56	    weak:
20.58/5.56	     a(a(c(x1))) -> a(b(c(x1)))
20.58/5.56	     a(c(c(x1))) -> c(b(a(x1)))
20.58/5.56	    Arctic Interpretation Processor:
20.58/5.56	     dimension: 1
20.58/5.56	     interpretation:
20.58/5.56	      [c](x0) = 1x0,
20.58/5.56	      
20.58/5.56	      [b](x0) = x0,
20.58/5.56	      
20.58/5.56	      [a](x0) = x0
20.58/5.56	     orientation:
20.58/5.56	      b(a(c(x1))) = 1x1 >= 1x1 = a(a(c(x1)))
20.58/5.56	      
20.58/5.56	      b(b(a(x1))) = x1 >= x1 = a(b(a(x1)))
20.58/5.56	      
20.58/5.56	      a(a(c(x1))) = 1x1 >= 1x1 = a(b(c(x1)))
20.58/5.56	      
20.58/5.56	      a(c(c(x1))) = 2x1 >= 1x1 = c(b(a(x1)))
20.58/5.56	     problem:
20.58/5.56	      strict:
20.58/5.56	       b(a(c(x1))) -> a(a(c(x1)))
20.58/5.56	       b(b(a(x1))) -> a(b(a(x1)))
20.58/5.56	      weak:
20.58/5.56	       a(a(c(x1))) -> a(b(c(x1)))
20.58/5.56	     String Reversal Processor:
20.58/5.56	      strict:
20.58/5.56	       c(a(b(x1))) -> c(a(a(x1)))
20.58/5.56	       a(b(b(x1))) -> a(b(a(x1)))
20.58/5.56	      weak:
20.58/5.56	       c(a(a(x1))) -> c(b(a(x1)))
20.58/5.56	      Bounds Processor:
20.58/5.56	       bound: 1
20.58/5.56	       enrichment: match-rt
20.58/5.56	       automaton:
20.58/5.56	        final states: {4}
20.58/5.56	        transitions:
20.58/5.56	         c1(29) -> 30*
20.58/5.56	         c1(11) -> 12*
20.58/5.56	         a1(10) -> 11*
20.58/5.56	         a1(9) -> 10*
20.58/5.56	         b1(23) -> 24*
20.58/5.56	         c0(4) -> 4*
20.58/5.56	         a0(4) -> 4*
20.58/5.56	         b0(4) -> 4*
20.58/5.56	         4 -> 9*
20.58/5.56	         10 -> 23*
20.58/5.56	         12 -> 4*
20.58/5.56	         24 -> 29,9
20.58/5.56	         30 -> 12*
20.58/5.56	       problem:
20.58/5.56	        strict:
20.58/5.56	         a(b(b(x1))) -> a(b(a(x1)))
20.58/5.56	        weak:
20.58/5.56	         c(a(a(x1))) -> c(b(a(x1)))
20.58/5.56	       Matrix Interpretation Processor: dim=2
20.58/5.56	        
20.58/5.56	        interpretation:
20.58/5.56	                   [2 0]     [0]
20.58/5.56	         [c](x0) = [1 0]x0 + [2],
20.58/5.56	         
20.58/5.56	                   [1 1]     [0]
20.58/5.56	         [b](x0) = [0 0]x0 + [2],
20.58/5.56	         
20.58/5.56	                   [1 0]  
20.58/5.56	         [a](x0) = [0 0]x0
20.58/5.56	        orientation:
20.58/5.56	                       [1 1]     [2]    [1 0]                
20.58/5.56	         a(b(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 = a(b(a(x1)))
20.58/5.56	         
20.58/5.56	                       [2 0]     [0]    [2 0]     [0]              
20.58/5.56	         c(a(a(x1))) = [1 0]x1 + [2] >= [1 0]x1 + [2] = c(b(a(x1)))
20.58/5.56	        problem:
20.58/5.56	         strict:
20.58/5.56	          
20.58/5.56	         weak:
20.58/5.56	          c(a(a(x1))) -> c(b(a(x1)))
20.58/5.56	        Qed
20.58/5.56	EOF