166.01/42.46	YES
166.01/42.46	
166.01/42.46	Problem:
166.01/42.46	 a(b(x1)) -> x1
166.01/42.46	 a(c(x1)) -> b(b(c(c(a(a(x1))))))
166.01/42.46	 b(c(x1)) -> x1
166.01/42.46	
166.01/42.46	Proof:
166.01/42.46	 String Reversal Processor:
166.01/42.46	  b(a(x1)) -> x1
166.01/42.46	  c(a(x1)) -> a(a(c(c(b(b(x1))))))
166.01/42.46	  c(b(x1)) -> x1
166.01/42.46	  DP Processor:
166.01/42.46	   DPs:
166.01/42.46	    c#(a(x1)) -> b#(x1)
166.01/42.46	    c#(a(x1)) -> b#(b(x1))
166.01/42.46	    c#(a(x1)) -> c#(b(b(x1)))
166.01/42.46	    c#(a(x1)) -> c#(c(b(b(x1))))
166.01/42.46	   TRS:
166.01/42.46	    b(a(x1)) -> x1
166.01/42.46	    c(a(x1)) -> a(a(c(c(b(b(x1))))))
166.01/42.46	    c(b(x1)) -> x1
166.01/42.46	   TDG Processor:
166.01/42.46	    DPs:
166.01/42.46	     c#(a(x1)) -> b#(x1)
166.01/42.46	     c#(a(x1)) -> b#(b(x1))
166.01/42.46	     c#(a(x1)) -> c#(b(b(x1)))
166.01/42.46	     c#(a(x1)) -> c#(c(b(b(x1))))
166.01/42.46	    TRS:
166.01/42.46	     b(a(x1)) -> x1
166.01/42.46	     c(a(x1)) -> a(a(c(c(b(b(x1))))))
166.01/42.46	     c(b(x1)) -> x1
166.01/42.46	    graph:
166.01/42.46	     c#(a(x1)) -> c#(c(b(b(x1)))) -> c#(a(x1)) -> c#(c(b(b(x1))))
166.01/42.46	     c#(a(x1)) -> c#(c(b(b(x1)))) -> c#(a(x1)) -> c#(b(b(x1)))
166.01/42.46	     c#(a(x1)) -> c#(c(b(b(x1)))) -> c#(a(x1)) -> b#(b(x1))
166.01/42.46	     c#(a(x1)) -> c#(c(b(b(x1)))) -> c#(a(x1)) -> b#(x1)
166.01/42.46	     c#(a(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> c#(c(b(b(x1))))
166.01/42.46	     c#(a(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> c#(b(b(x1)))
166.01/42.46	     c#(a(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> b#(b(x1))
166.01/42.46	     c#(a(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> b#(x1)
166.01/42.46	    SCC Processor:
166.01/42.46	     #sccs: 1
166.01/42.46	     #rules: 2
166.01/42.46	     #arcs: 8/16
166.01/42.46	     DPs:
166.01/42.46	      c#(a(x1)) -> c#(c(b(b(x1))))
166.01/42.46	      c#(a(x1)) -> c#(b(b(x1)))
166.01/42.46	     TRS:
166.01/42.46	      b(a(x1)) -> x1
166.01/42.46	      c(a(x1)) -> a(a(c(c(b(b(x1))))))
166.01/42.46	      c(b(x1)) -> x1
166.01/42.46	     Arctic Interpretation Processor:
166.01/42.46	      dimension: 1
166.01/42.46	      usable rules:
166.01/42.46	       b(a(x1)) -> x1
166.01/42.46	       c(a(x1)) -> a(a(c(c(b(b(x1))))))
166.01/42.46	       c(b(x1)) -> x1
166.01/42.46	      interpretation:
166.01/42.46	       [c#](x0) = 8x0 + 0,
166.01/42.46	       
166.01/42.46	       [c](x0) = 1x0 + 2,
166.01/42.46	       
166.01/42.46	       [a](x0) = 1x0 + 4,
166.01/42.46	       
166.01/42.46	       [b](x0) = -1x0 + 0
166.01/42.46	      orientation:
166.01/42.46	       c#(a(x1)) = 9x1 + 12 >= 7x1 + 10 = c#(c(b(b(x1))))
166.01/42.46	       
166.01/42.46	       c#(a(x1)) = 9x1 + 12 >= 6x1 + 8 = c#(b(b(x1)))
166.01/42.46	       
166.01/42.46	       b(a(x1)) = x1 + 3 >= x1 = x1
166.01/42.46	       
166.01/42.46	       c(a(x1)) = 2x1 + 5 >= 2x1 + 5 = a(a(c(c(b(b(x1))))))
166.01/42.46	       
166.01/42.46	       c(b(x1)) = x1 + 2 >= x1 = x1
166.01/42.46	      problem:
166.01/42.46	       DPs:
166.01/42.46	        
166.01/42.46	       TRS:
166.01/42.46	        b(a(x1)) -> x1
166.01/42.46	        c(a(x1)) -> a(a(c(c(b(b(x1))))))
166.01/42.46	        c(b(x1)) -> x1
166.01/42.46	      Qed
166.01/42.47	EOF