171.63/43.91	YES
171.63/43.91	
171.63/43.91	Problem:
171.63/43.91	 a(x1) -> b(c(x1))
171.63/43.91	 a(c(b(x1))) -> b(a(a(c(x1))))
171.63/43.91	 b(b(x1)) -> x1
171.63/43.91	
171.63/43.91	Proof:
171.63/43.91	 DP Processor:
171.63/43.91	  DPs:
171.63/43.91	   a#(x1) -> b#(c(x1))
171.63/43.91	   a#(c(b(x1))) -> a#(c(x1))
171.63/43.91	   a#(c(b(x1))) -> a#(a(c(x1)))
171.63/43.91	   a#(c(b(x1))) -> b#(a(a(c(x1))))
171.63/43.91	  TRS:
171.63/43.91	   a(x1) -> b(c(x1))
171.63/43.91	   a(c(b(x1))) -> b(a(a(c(x1))))
171.63/43.91	   b(b(x1)) -> x1
171.63/43.91	  TDG Processor:
171.63/43.91	   DPs:
171.63/43.91	    a#(x1) -> b#(c(x1))
171.63/43.91	    a#(c(b(x1))) -> a#(c(x1))
171.63/43.91	    a#(c(b(x1))) -> a#(a(c(x1)))
171.63/43.91	    a#(c(b(x1))) -> b#(a(a(c(x1))))
171.63/43.91	   TRS:
171.63/43.91	    a(x1) -> b(c(x1))
171.63/43.91	    a(c(b(x1))) -> b(a(a(c(x1))))
171.63/43.91	    b(b(x1)) -> x1
171.63/43.91	   graph:
171.63/43.91	    a#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> b#(a(a(c(x1))))
171.63/43.91	    a#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> a#(a(c(x1)))
171.63/43.91	    a#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> a#(c(x1))
171.63/43.91	    a#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> b#(c(x1))
171.63/43.91	    a#(c(b(x1))) -> a#(a(c(x1))) -> a#(c(b(x1))) -> b#(a(a(c(x1))))
171.63/43.91	    a#(c(b(x1))) -> a#(a(c(x1))) -> a#(c(b(x1))) -> a#(a(c(x1)))
171.63/43.91	    a#(c(b(x1))) -> a#(a(c(x1))) -> a#(c(b(x1))) -> a#(c(x1))
171.63/43.91	    a#(c(b(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(c(x1))
171.63/43.91	   SCC Processor:
171.63/43.91	    #sccs: 1
171.63/43.91	    #rules: 2
171.63/43.91	    #arcs: 8/16
171.63/43.91	    DPs:
171.63/43.91	     a#(c(b(x1))) -> a#(c(x1))
171.63/43.91	     a#(c(b(x1))) -> a#(a(c(x1)))
171.63/43.91	    TRS:
171.63/43.91	     a(x1) -> b(c(x1))
171.63/43.91	     a(c(b(x1))) -> b(a(a(c(x1))))
171.63/43.91	     b(b(x1)) -> x1
171.63/43.91	    Arctic Interpretation Processor:
171.63/43.91	     dimension: 2
171.63/43.91	     usable rules:
171.63/43.91	      a(x1) -> b(c(x1))
171.63/43.91	      a(c(b(x1))) -> b(a(a(c(x1))))
171.63/43.91	      b(b(x1)) -> x1
171.63/43.91	     interpretation:
171.63/43.91	      [a#](x0) = [0  -&]x0 + [1],
171.63/43.91	      
171.63/43.91	                [-& 0 ]     [0]
171.63/43.91	      [b](x0) = [0  1 ]x0 + [2],
171.63/43.91	      
171.63/43.91	                [-& 0 ]     [0]
171.63/43.91	      [c](x0) = [0  -&]x0 + [0],
171.63/43.91	      
171.63/43.91	                [0  -&]     [0]
171.63/43.91	      [a](x0) = [1  0 ]x0 + [2]
171.63/43.91	     orientation:
171.63/43.91	      a#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = a#(c(x1))
171.63/43.91	      
171.63/43.91	      a#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = a#(a(c(x1)))
171.63/43.91	      
171.63/43.91	              [0  -&]     [0]    [0  -&]     [0]           
171.63/43.91	      a(x1) = [1  0 ]x1 + [2] >= [1  0 ]x1 + [2] = b(c(x1))
171.63/43.91	      
171.63/43.91	                    [0 1]     [2]    [0 1]     [2]                 
171.63/43.91	      a(c(b(x1))) = [1 2]x1 + [3] >= [1 2]x1 + [3] = b(a(a(c(x1))))
171.63/43.91	      
171.63/43.91	                 [0 1]     [2]           
171.63/43.91	      b(b(x1)) = [1 2]x1 + [3] >= x1 = x1
171.63/43.91	     problem:
171.63/43.91	      DPs:
171.63/43.91	       
171.63/43.91	      TRS:
171.63/43.91	       a(x1) -> b(c(x1))
171.63/43.91	       a(c(b(x1))) -> b(a(a(c(x1))))
171.63/43.91	       b(b(x1)) -> x1
171.63/43.91	     Qed
171.90/43.92	EOF