169.15/43.30	YES
169.15/43.30	
169.15/43.30	Problem:
169.15/43.30	 a(x1) -> b(c(x1))
169.15/43.30	 a(b(x1)) -> x1
169.15/43.30	 a(b(b(x1))) -> b(b(a(a(x1))))
169.15/43.30	
169.15/43.30	Proof:
169.15/43.30	 DP Processor:
169.15/43.30	  DPs:
169.15/43.30	   a#(b(b(x1))) -> a#(x1)
169.15/43.30	   a#(b(b(x1))) -> a#(a(x1))
169.15/43.30	  TRS:
169.15/43.30	   a(x1) -> b(c(x1))
169.15/43.30	   a(b(x1)) -> x1
169.15/43.30	   a(b(b(x1))) -> b(b(a(a(x1))))
169.15/43.30	  Arctic Interpretation Processor:
169.15/43.30	   dimension: 2
169.15/43.30	   usable rules:
169.15/43.30	    a(x1) -> b(c(x1))
169.15/43.30	    a(b(x1)) -> x1
169.15/43.30	    a(b(b(x1))) -> b(b(a(a(x1))))
169.15/43.30	   interpretation:
169.15/43.30	    [a#](x0) = [0 0]x0,
169.15/43.30	    
169.15/43.30	              [0 0]     [1]
169.15/43.30	    [b](x0) = [1 0]x0 + [1],
169.15/43.30	    
169.15/43.30	              [0]
169.15/43.30	    [c](x0) = [1],
169.15/43.30	    
169.15/43.30	              [-& 0 ]     [1]
169.15/43.30	    [a](x0) = [-& 0 ]x0 + [1]
169.15/43.30	   orientation:
169.15/43.30	    a#(b(b(x1))) = [1 1]x1 + [2] >= [0 0]x1 = a#(x1)
169.15/43.30	    
169.15/43.30	    a#(b(b(x1))) = [1 1]x1 + [2] >= [-& 0 ]x1 + [1] = a#(a(x1))
169.15/43.30	    
169.15/43.30	            [-& 0 ]     [1]    [1]           
169.15/43.30	    a(x1) = [-& 0 ]x1 + [1] >= [1] = b(c(x1))
169.15/43.30	    
169.15/43.30	               [1 0]     [1]           
169.15/43.30	    a(b(x1)) = [1 0]x1 + [1] >= x1 = x1
169.15/43.30	    
169.15/43.30	                  [1 1]     [2]    [-& 1 ]     [2]                 
169.15/43.30	    a(b(b(x1))) = [1 1]x1 + [2] >= [-& 1 ]x1 + [2] = b(b(a(a(x1))))
169.15/43.30	   problem:
169.15/43.30	    DPs:
169.15/43.30	     
169.15/43.30	    TRS:
169.15/43.30	     a(x1) -> b(c(x1))
169.15/43.30	     a(b(x1)) -> x1
169.15/43.30	     a(b(b(x1))) -> b(b(a(a(x1))))
169.15/43.30	   Qed
169.15/43.31	EOF