168.51/43.00	YES
168.51/43.00	
168.51/43.00	Problem:
168.51/43.00	 a(x1) -> x1
168.51/43.00	 a(x1) -> b(c(x1))
168.51/43.00	 a(b(b(x1))) -> b(b(a(a(x1))))
168.51/43.00	
168.51/43.00	Proof:
168.51/43.00	 DP Processor:
168.51/43.00	  DPs:
168.51/43.00	   a#(b(b(x1))) -> a#(x1)
168.51/43.00	   a#(b(b(x1))) -> a#(a(x1))
168.51/43.00	  TRS:
168.51/43.00	   a(x1) -> x1
168.51/43.00	   a(x1) -> b(c(x1))
168.51/43.00	   a(b(b(x1))) -> b(b(a(a(x1))))
168.51/43.00	  Arctic Interpretation Processor:
168.51/43.00	   dimension: 2
168.51/43.00	   usable rules:
168.51/43.00	    a(x1) -> x1
168.51/43.00	    a(x1) -> b(c(x1))
168.51/43.00	    a(b(b(x1))) -> b(b(a(a(x1))))
168.51/43.00	   interpretation:
168.51/43.00	    [a#](x0) = [1 0]x0 + [0],
168.51/43.00	    
168.51/43.00	              [-& 1 ]     [0]
168.51/43.00	    [b](x0) = [0  -&]x0 + [3],
168.51/43.00	    
168.51/43.00	              [0  0 ]     [1]
168.51/43.00	    [c](x0) = [-& -&]x0 + [0],
168.51/43.00	    
168.51/43.00	              [0  -&]     [3]
168.51/43.00	    [a](x0) = [1  0 ]x0 + [3]
168.51/43.00	   orientation:
168.51/43.00	    a#(b(b(x1))) = [2 1]x1 + [5] >= [1 0]x1 + [0] = a#(x1)
168.51/43.00	    
168.51/43.00	    a#(b(b(x1))) = [2 1]x1 + [5] >= [1 0]x1 + [4] = a#(a(x1))
168.51/43.00	    
168.51/43.00	            [0  -&]     [3]           
168.51/43.00	    a(x1) = [1  0 ]x1 + [3] >= x1 = x1
168.51/43.00	    
168.51/43.00	            [0  -&]     [3]    [-& -&]     [1]           
168.51/43.00	    a(x1) = [1  0 ]x1 + [3] >= [0  0 ]x1 + [3] = b(c(x1))
168.51/43.00	    
168.51/43.00	                  [1  -&]     [4]    [1  -&]     [4]                 
168.51/43.00	    a(b(b(x1))) = [2  1 ]x1 + [5] >= [2  1 ]x1 + [5] = b(b(a(a(x1))))
168.51/43.00	   problem:
168.51/43.00	    DPs:
168.51/43.00	     
168.51/43.00	    TRS:
168.51/43.00	     a(x1) -> x1
168.51/43.00	     a(x1) -> b(c(x1))
168.51/43.00	     a(b(b(x1))) -> b(b(a(a(x1))))
168.51/43.00	   Qed
168.51/43.01	EOF