16.53/4.55	YES
16.53/4.56	
16.53/4.56	Problem:
16.53/4.56	 strict:
16.53/4.56	  c(a(b(x1))) -> a(b(c(x1)))
16.53/4.56	  a(b(a(x1))) -> c(a(a(x1)))
16.53/4.56	  c(c(c(x1))) -> b(c(c(x1)))
16.53/4.56	  b(b(a(x1))) -> b(b(b(x1)))
16.53/4.56	 weak:
16.53/4.56	  a(c(b(x1))) -> c(b(c(x1)))
16.53/4.56	  a(c(b(x1))) -> b(b(c(x1)))
16.53/4.56	
16.53/4.56	Proof:
16.53/4.56	 Arctic Interpretation Processor:
16.53/4.56	  dimension: 1
16.53/4.56	  interpretation:
16.53/4.56	   [c](x0) = 9x0,
16.53/4.56	   
16.53/4.56	   [a](x0) = 10x0,
16.53/4.56	   
16.53/4.56	   [b](x0) = 9x0
16.53/4.56	  orientation:
16.53/4.56	   c(a(b(x1))) = 28x1 >= 28x1 = a(b(c(x1)))
16.53/4.56	   
16.53/4.56	   a(b(a(x1))) = 29x1 >= 29x1 = c(a(a(x1)))
16.53/4.56	   
16.53/4.56	   c(c(c(x1))) = 27x1 >= 27x1 = b(c(c(x1)))
16.53/4.56	   
16.53/4.56	   b(b(a(x1))) = 28x1 >= 27x1 = b(b(b(x1)))
16.53/4.56	   
16.53/4.56	   a(c(b(x1))) = 28x1 >= 27x1 = c(b(c(x1)))
16.53/4.56	   
16.53/4.56	   a(c(b(x1))) = 28x1 >= 27x1 = b(b(c(x1)))
16.53/4.56	  problem:
16.53/4.56	   strict:
16.53/4.56	    c(a(b(x1))) -> a(b(c(x1)))
16.53/4.56	    a(b(a(x1))) -> c(a(a(x1)))
16.53/4.56	    c(c(c(x1))) -> b(c(c(x1)))
16.53/4.56	   weak:
16.53/4.56	    
16.53/4.56	  Matrix Interpretation Processor: dim=2
16.53/4.56	   
16.53/4.56	   interpretation:
16.53/4.56	              [1 0]  
16.53/4.56	    [c](x0) = [1 0]x0,
16.53/4.56	    
16.53/4.56	              [1 1]     [1]
16.53/4.56	    [a](x0) = [1 1]x0 + [0],
16.53/4.56	    
16.53/4.56	              [1 0]  
16.53/4.56	    [b](x0) = [1 0]x0
16.53/4.56	   orientation:
16.53/4.56	                  [2 0]     [1]    [2 0]     [1]              
16.53/4.56	    c(a(b(x1))) = [2 0]x1 + [1] >= [2 0]x1 + [0] = a(b(c(x1)))
16.53/4.56	    
16.53/4.56	                  [2 2]     [3]    [2 2]     [2]              
16.53/4.56	    a(b(a(x1))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = c(a(a(x1)))
16.53/4.56	    
16.53/4.56	                  [1 0]      [1 0]                
16.53/4.56	    c(c(c(x1))) = [1 0]x1 >= [1 0]x1 = b(c(c(x1)))
16.53/4.56	   problem:
16.53/4.56	    strict:
16.53/4.56	     c(a(b(x1))) -> a(b(c(x1)))
16.53/4.56	     c(c(c(x1))) -> b(c(c(x1)))
16.53/4.56	    weak:
16.53/4.56	     
16.53/4.56	   Arctic Interpretation Processor:
16.53/4.56	    dimension: 1
16.53/4.56	    interpretation:
16.53/4.56	     [c](x0) = 9x0,
16.53/4.56	     
16.53/4.56	     [a](x0) = 2x0,
16.53/4.56	     
16.53/4.56	     [b](x0) = 3x0
16.53/4.56	    orientation:
16.53/4.56	     c(a(b(x1))) = 14x1 >= 14x1 = a(b(c(x1)))
16.53/4.56	     
16.53/4.56	     c(c(c(x1))) = 27x1 >= 21x1 = b(c(c(x1)))
16.53/4.56	    problem:
16.53/4.56	     strict:
16.53/4.56	      c(a(b(x1))) -> a(b(c(x1)))
16.53/4.56	     weak:
16.53/4.56	      
16.53/4.56	    Matrix Interpretation Processor: dim=2
16.53/4.56	     
16.53/4.56	     interpretation:
16.53/4.56	                [2 0]     [1]
16.53/4.56	      [c](x0) = [0 2]x0 + [0],
16.53/4.56	      
16.53/4.56	                [1 1]  
16.53/4.56	      [a](x0) = [1 0]x0,
16.53/4.56	      
16.53/4.56	                     [1]
16.53/4.56	      [b](x0) = x0 + [0]
16.53/4.56	     orientation:
16.53/4.56	                    [2 2]     [3]    [2 2]     [2]              
16.53/4.56	      c(a(b(x1))) = [2 0]x1 + [2] >= [2 0]x1 + [2] = a(b(c(x1)))
16.53/4.56	     problem:
16.53/4.56	      strict:
16.53/4.56	       
16.53/4.56	      weak:
16.53/4.56	       
16.53/4.56	     Qed
16.53/4.56	EOF