8.29/2.41	YES
8.29/2.41	
8.29/2.41	Problem:
8.29/2.41	 strict:
8.29/2.41	  a(a(b(x1))) -> b(a(x1))
8.29/2.41	  c(b(x1)) -> b(c(a(x1)))
8.29/2.41	 weak:
8.29/2.41	  a(x1) -> a(c(a(x1)))
8.29/2.41	
8.29/2.41	Proof:
8.29/2.41	 Matrix Interpretation Processor: dim=2
8.29/2.41	  
8.29/2.41	  interpretation:
8.29/2.41	             [1 0]  
8.29/2.41	   [c](x0) = [0 0]x0,
8.29/2.41	   
8.29/2.41	             [1 1]  
8.29/2.41	   [a](x0) = [1 1]x0,
8.29/2.41	   
8.29/2.41	             [1 1]     [1]
8.29/2.41	   [b](x0) = [0 0]x0 + [0]
8.29/2.41	  orientation:
8.29/2.41	                 [2 2]     [2]    [2 2]     [1]           
8.29/2.41	   a(a(b(x1))) = [2 2]x1 + [2] >= [0 0]x1 + [0] = b(a(x1))
8.29/2.41	   
8.29/2.41	              [1 1]     [1]    [1 1]     [1]              
8.29/2.41	   c(b(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = b(c(a(x1)))
8.29/2.41	   
8.29/2.41	           [1 1]      [1 1]                
8.29/2.41	   a(x1) = [1 1]x1 >= [1 1]x1 = a(c(a(x1)))
8.29/2.41	  problem:
8.29/2.41	   strict:
8.29/2.41	    c(b(x1)) -> b(c(a(x1)))
8.29/2.41	   weak:
8.29/2.41	    a(x1) -> a(c(a(x1)))
8.29/2.41	  Arctic Interpretation Processor:
8.29/2.41	   dimension: 2
8.29/2.41	   interpretation:
8.29/2.41	              [0 7]  
8.29/2.41	    [c](x0) = [6 3]x0,
8.29/2.41	    
8.29/2.41	              [0  -&]  
8.29/2.41	    [a](x0) = [-& -&]x0,
8.29/2.41	    
8.29/2.41	              [2 6]  
8.29/2.41	    [b](x0) = [6 0]x0
8.29/2.41	   orientation:
8.29/2.41	               [13 7 ]      [12 -&]                
8.29/2.41	    c(b(x1)) = [9  12]x1 >= [6  -&]x1 = b(c(a(x1)))
8.29/2.41	    
8.29/2.41	            [0  -&]      [0  -&]                
8.29/2.41	    a(x1) = [-& -&]x1 >= [-& -&]x1 = a(c(a(x1)))
8.29/2.41	   problem:
8.29/2.41	    strict:
8.29/2.41	     
8.29/2.41	    weak:
8.29/2.41	     a(x1) -> a(c(a(x1)))
8.29/2.41	   Qed
8.29/2.42	EOF