176.09/44.68	YES
176.36/44.69	
176.36/44.69	Problem:
176.36/44.69	 a(x1) -> x1
176.36/44.69	 a(b(b(x1))) -> b(b(a(b(c(a(x1))))))
176.36/44.69	 b(c(x1)) -> x1
176.36/44.69	
176.36/44.69	Proof:
176.36/44.69	 DP Processor:
176.36/44.69	  DPs:
176.36/44.69	   a#(b(b(x1))) -> a#(x1)
176.36/44.69	   a#(b(b(x1))) -> b#(c(a(x1)))
176.36/44.69	   a#(b(b(x1))) -> a#(b(c(a(x1))))
176.36/44.69	   a#(b(b(x1))) -> b#(a(b(c(a(x1)))))
176.36/44.69	   a#(b(b(x1))) -> b#(b(a(b(c(a(x1))))))
176.36/44.69	  TRS:
176.36/44.69	   a(x1) -> x1
176.36/44.69	   a(b(b(x1))) -> b(b(a(b(c(a(x1))))))
176.36/44.69	   b(c(x1)) -> x1
176.36/44.69	  TDG Processor:
176.36/44.69	   DPs:
176.36/44.69	    a#(b(b(x1))) -> a#(x1)
176.36/44.69	    a#(b(b(x1))) -> b#(c(a(x1)))
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1))))
176.36/44.69	    a#(b(b(x1))) -> b#(a(b(c(a(x1)))))
176.36/44.69	    a#(b(b(x1))) -> b#(b(a(b(c(a(x1))))))
176.36/44.69	   TRS:
176.36/44.69	    a(x1) -> x1
176.36/44.69	    a(b(b(x1))) -> b(b(a(b(c(a(x1))))))
176.36/44.69	    b(c(x1)) -> x1
176.36/44.69	   graph:
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1)))) ->
176.36/44.69	    a#(b(b(x1))) -> b#(b(a(b(c(a(x1))))))
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1)))) ->
176.36/44.69	    a#(b(b(x1))) -> b#(a(b(c(a(x1)))))
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1)))) ->
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1))))
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> b#(c(a(x1)))
176.36/44.69	    a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> a#(x1)
176.36/44.69	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(b(a(b(c(a(x1))))))
176.36/44.69	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(a(b(c(a(x1)))))
176.36/44.69	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(b(c(a(x1))))
176.36/44.69	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(c(a(x1)))
176.36/44.69	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
176.36/44.69	   SCC Processor:
176.36/44.69	    #sccs: 1
176.36/44.69	    #rules: 2
176.36/44.69	    #arcs: 10/25
176.36/44.69	    DPs:
176.36/44.69	     a#(b(b(x1))) -> a#(b(c(a(x1))))
176.36/44.69	     a#(b(b(x1))) -> a#(x1)
176.36/44.69	    TRS:
176.36/44.69	     a(x1) -> x1
176.36/44.69	     a(b(b(x1))) -> b(b(a(b(c(a(x1))))))
176.36/44.69	     b(c(x1)) -> x1
176.36/44.69	    Arctic Interpretation Processor:
176.36/44.69	     dimension: 2
176.36/44.69	     usable rules:
176.36/44.69	      a(x1) -> x1
176.36/44.69	      a(b(b(x1))) -> b(b(a(b(c(a(x1))))))
176.36/44.69	      b(c(x1)) -> x1
176.36/44.69	     interpretation:
176.36/44.69	      [a#](x0) = [-& 2 ]x0 + [0],
176.36/44.69	      
176.36/44.69	                [-& -&]     [0]
176.36/44.69	      [c](x0) = [0  0 ]x0 + [2],
176.36/44.69	      
176.36/44.69	                [-& 0 ]     [3 ]
176.36/44.69	      [b](x0) = [2  0 ]x0 + [-&],
176.36/44.69	      
176.36/44.69	                [0 0]     [0]
176.36/44.69	      [a](x0) = [0 0]x0 + [0]
176.36/44.69	     orientation:
176.36/44.69	      a#(b(b(x1))) = [4 4]x1 + [7] >= [2 2]x1 + [4] = a#(b(c(a(x1))))
176.36/44.69	      
176.36/44.69	      a#(b(b(x1))) = [4 4]x1 + [7] >= [-& 2 ]x1 + [0] = a#(x1)
176.36/44.69	      
176.36/44.69	              [0 0]     [0]           
176.36/44.69	      a(x1) = [0 0]x1 + [0] >= x1 = x1
176.36/44.69	      
176.36/44.69	                    [2 2]     [5]    [2 2]     [5]                       
176.36/44.69	      a(b(b(x1))) = [2 2]x1 + [5] >= [2 2]x1 + [5] = b(b(a(b(c(a(x1))))))
176.36/44.69	      
176.36/44.69	                 [0 0]     [3]           
176.36/44.69	      b(c(x1)) = [0 0]x1 + [2] >= x1 = x1
176.36/44.69	     problem:
176.36/44.69	      DPs:
176.36/44.69	       
176.36/44.69	      TRS:
176.36/44.69	       a(x1) -> x1
176.36/44.69	       a(b(b(x1))) -> b(b(a(b(c(a(x1))))))
176.36/44.69	       b(c(x1)) -> x1
176.36/44.69	     Qed
176.36/44.69	EOF