167.78/42.92	YES
167.78/42.92	
167.78/42.92	Problem:
167.78/42.92	 a(x1) -> x1
167.78/42.92	 a(b(x1)) -> c(b(x1))
167.78/42.92	 a(c(c(x1))) -> c(c(a(a(x1))))
167.78/42.92	
167.78/42.92	Proof:
167.78/42.92	 DP Processor:
167.78/42.92	  DPs:
167.78/42.92	   a#(c(c(x1))) -> a#(x1)
167.78/42.92	   a#(c(c(x1))) -> a#(a(x1))
167.78/42.92	  TRS:
167.78/42.92	   a(x1) -> x1
167.78/42.92	   a(b(x1)) -> c(b(x1))
167.78/42.92	   a(c(c(x1))) -> c(c(a(a(x1))))
167.78/42.92	  Arctic Interpretation Processor:
167.78/42.92	   dimension: 2
167.78/42.92	   usable rules:
167.78/42.92	    a(x1) -> x1
167.78/42.92	    a(b(x1)) -> c(b(x1))
167.78/42.92	    a(c(c(x1))) -> c(c(a(a(x1))))
167.78/42.92	   interpretation:
167.78/42.92	    [a#](x0) = [-& 2 ]x0 + [0],
167.78/42.92	    
167.78/42.92	              [-& 1 ]     [0]
167.78/42.92	    [c](x0) = [0  -&]x0 + [0],
167.78/42.92	    
167.78/42.92	              [-& -&]     [0]
167.78/42.92	    [b](x0) = [0  1 ]x0 + [3],
167.78/42.92	    
167.78/42.92	              [0  2 ]     [1 ]
167.78/42.92	    [a](x0) = [-& 0 ]x0 + [-&]
167.78/42.92	   orientation:
167.78/42.92	    a#(c(c(x1))) = [-& 3 ]x1 + [2] >= [-& 2 ]x1 + [0] = a#(x1)
167.78/42.92	    
167.78/42.92	    a#(c(c(x1))) = [-& 3 ]x1 + [2] >= [-& 2 ]x1 + [0] = a#(a(x1))
167.78/42.92	    
167.78/42.92	            [0  2 ]     [1 ]           
167.78/42.92	    a(x1) = [-& 0 ]x1 + [-&] >= x1 = x1
167.78/42.92	    
167.78/42.92	               [2 3]     [5]    [1  2 ]     [4]           
167.78/42.92	    a(b(x1)) = [0 1]x1 + [3] >= [-& -&]x1 + [0] = c(b(x1))
167.78/42.92	    
167.78/42.92	                  [1  3 ]     [2]    [1  3 ]     [2]                 
167.78/42.92	    a(c(c(x1))) = [-& 1 ]x1 + [0] >= [-& 1 ]x1 + [0] = c(c(a(a(x1))))
167.78/42.92	   problem:
167.78/42.92	    DPs:
167.78/42.92	     
167.78/42.92	    TRS:
167.78/42.92	     a(x1) -> x1
167.78/42.92	     a(b(x1)) -> c(b(x1))
167.78/42.92	     a(c(c(x1))) -> c(c(a(a(x1))))
167.78/42.92	   Qed
167.78/42.93	EOF