164.71/42.40	YES
164.71/42.41	
164.71/42.41	Problem:
164.71/42.41	 a(b(x1)) -> x1
164.71/42.41	 a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	 b(c(x1)) -> a(b(x1))
164.71/42.41	
164.71/42.41	Proof:
164.71/42.41	 DP Processor:
164.71/42.41	  DPs:
164.71/42.41	   a#(c(x1)) -> b#(c(c(x1)))
164.71/42.41	   b#(c(x1)) -> b#(x1)
164.71/42.41	   b#(c(x1)) -> a#(b(x1))
164.71/42.41	  TRS:
164.71/42.41	   a(b(x1)) -> x1
164.71/42.41	   a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	   b(c(x1)) -> a(b(x1))
164.71/42.41	  TDG Processor:
164.71/42.41	   DPs:
164.71/42.41	    a#(c(x1)) -> b#(c(c(x1)))
164.71/42.41	    b#(c(x1)) -> b#(x1)
164.71/42.41	    b#(c(x1)) -> a#(b(x1))
164.71/42.41	   TRS:
164.71/42.41	    a(b(x1)) -> x1
164.71/42.41	    a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	    b(c(x1)) -> a(b(x1))
164.71/42.41	   graph:
164.71/42.41	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(x1))
164.71/42.41	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
164.71/42.41	    b#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(c(c(x1)))
164.71/42.41	    a#(c(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> a#(b(x1))
164.71/42.41	    a#(c(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> b#(x1)
164.71/42.41	   Arctic Interpretation Processor:
164.71/42.41	    dimension: 1
164.71/42.41	    usable rules:
164.71/42.41	     a(b(x1)) -> x1
164.71/42.41	     a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	     b(c(x1)) -> a(b(x1))
164.71/42.41	    interpretation:
164.71/42.41	     [b#](x0) = 1x0 + 9,
164.71/42.41	     
164.71/42.41	     [a#](x0) = 2x0 + 3,
164.71/42.41	     
164.71/42.41	     [c](x0) = 1x0 + 7,
164.71/42.41	     
164.71/42.41	     [a](x0) = 1x0 + 0,
164.71/42.41	     
164.71/42.41	     [b](x0) = -1x0 + 0
164.71/42.41	    orientation:
164.71/42.41	     a#(c(x1)) = 3x1 + 9 >= 3x1 + 9 = b#(c(c(x1)))
164.71/42.41	     
164.71/42.41	     b#(c(x1)) = 2x1 + 9 >= 1x1 + 9 = b#(x1)
164.71/42.41	     
164.71/42.41	     b#(c(x1)) = 2x1 + 9 >= 1x1 + 3 = a#(b(x1))
164.71/42.41	     
164.71/42.41	     a(b(x1)) = x1 + 1 >= x1 = x1
164.71/42.41	     
164.71/42.41	     a(c(x1)) = 2x1 + 8 >= 2x1 + 8 = c(b(c(c(x1))))
164.71/42.41	     
164.71/42.41	     b(c(x1)) = x1 + 6 >= x1 + 1 = a(b(x1))
164.71/42.41	    problem:
164.71/42.41	     DPs:
164.71/42.41	      a#(c(x1)) -> b#(c(c(x1)))
164.71/42.41	      b#(c(x1)) -> b#(x1)
164.71/42.41	     TRS:
164.71/42.41	      a(b(x1)) -> x1
164.71/42.41	      a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	      b(c(x1)) -> a(b(x1))
164.71/42.41	    Restore Modifier:
164.71/42.41	     DPs:
164.71/42.41	      a#(c(x1)) -> b#(c(c(x1)))
164.71/42.41	      b#(c(x1)) -> b#(x1)
164.71/42.41	     TRS:
164.71/42.41	      a(b(x1)) -> x1
164.71/42.41	      a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	      b(c(x1)) -> a(b(x1))
164.71/42.41	     EDG Processor:
164.71/42.41	      DPs:
164.71/42.41	       a#(c(x1)) -> b#(c(c(x1)))
164.71/42.41	       b#(c(x1)) -> b#(x1)
164.71/42.41	      TRS:
164.71/42.41	       a(b(x1)) -> x1
164.71/42.41	       a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	       b(c(x1)) -> a(b(x1))
164.71/42.41	      graph:
164.71/42.41	       b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
164.71/42.41	       a#(c(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> b#(x1)
164.71/42.41	      SCC Processor:
164.71/42.41	       #sccs: 1
164.71/42.41	       #rules: 1
164.71/42.41	       #arcs: 2/4
164.71/42.41	       DPs:
164.71/42.41	        b#(c(x1)) -> b#(x1)
164.71/42.41	       TRS:
164.71/42.41	        a(b(x1)) -> x1
164.71/42.41	        a(c(x1)) -> c(b(c(c(x1))))
164.71/42.41	        b(c(x1)) -> a(b(x1))
164.71/42.41	       Usable Rule Processor:
164.71/42.41	        DPs:
164.71/42.41	         b#(c(x1)) -> b#(x1)
164.71/42.41	        TRS:
164.71/42.41	         
164.71/42.41	        Arctic Interpretation Processor:
164.71/42.41	         dimension: 4
164.71/42.41	         usable rules:
164.71/42.41	          
164.71/42.41	         interpretation:
164.71/42.41	          [b#](x0) = [0  -& -& -&]x0,
164.71/42.41	          
164.71/42.41	                    [1 0 0 0]     [0]
164.71/42.41	                    [0 0 0 0]     [0]
164.71/42.41	          [c](x0) = [1 0 0 0]x0 + [0]
164.71/42.41	                    [0 0 0 0]     [0]
164.71/42.41	         orientation:
164.71/42.41	          b#(c(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = b#(x1)
164.71/42.41	         problem:
164.71/42.41	          DPs:
164.71/42.41	           
164.71/42.41	          TRS:
164.71/42.41	           
164.71/42.41	         Qed
166.27/42.41	EOF