168.96/43.11	YES
168.96/43.12	
168.96/43.12	Problem:
168.96/43.12	 a(x1) -> x1
168.96/43.12	 a(b(x1)) -> b(b(b(a(a(c(x1))))))
168.96/43.12	 b(x1) -> x1
168.96/43.12	 c(c(x1)) -> x1
168.96/43.12	
168.96/43.12	Proof:
168.96/43.12	 String Reversal Processor:
168.96/43.12	  a(x1) -> x1
168.96/43.12	  b(a(x1)) -> c(a(a(b(b(b(x1))))))
168.96/43.12	  b(x1) -> x1
168.96/43.12	  c(c(x1)) -> x1
168.96/43.12	  DP Processor:
168.96/43.12	   DPs:
168.96/43.12	    b#(a(x1)) -> b#(x1)
168.96/43.12	    b#(a(x1)) -> b#(b(x1))
168.96/43.12	    b#(a(x1)) -> b#(b(b(x1)))
168.96/43.12	    b#(a(x1)) -> a#(b(b(b(x1))))
168.96/43.12	    b#(a(x1)) -> a#(a(b(b(b(x1)))))
168.96/43.12	    b#(a(x1)) -> c#(a(a(b(b(b(x1))))))
168.96/43.12	   TRS:
168.96/43.12	    a(x1) -> x1
168.96/43.12	    b(a(x1)) -> c(a(a(b(b(b(x1))))))
168.96/43.12	    b(x1) -> x1
168.96/43.12	    c(c(x1)) -> x1
168.96/43.12	   TDG Processor:
168.96/43.12	    DPs:
168.96/43.12	     b#(a(x1)) -> b#(x1)
168.96/43.12	     b#(a(x1)) -> b#(b(x1))
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1)))
168.96/43.12	     b#(a(x1)) -> a#(b(b(b(x1))))
168.96/43.12	     b#(a(x1)) -> a#(a(b(b(b(x1)))))
168.96/43.12	     b#(a(x1)) -> c#(a(a(b(b(b(x1))))))
168.96/43.12	    TRS:
168.96/43.12	     a(x1) -> x1
168.96/43.12	     b(a(x1)) -> c(a(a(b(b(b(x1))))))
168.96/43.12	     b(x1) -> x1
168.96/43.12	     c(c(x1)) -> x1
168.96/43.12	    graph:
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> c#(a(a(b(b(b(x1))))))
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> a#(a(b(b(b(x1)))))
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> a#(b(b(b(x1))))
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(b(b(x1)))
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(b(x1))
168.96/43.12	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(x1)
168.96/43.12	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(a(b(b(b(x1))))))
168.96/43.12	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(a(b(b(b(x1)))))
168.96/43.12	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(b(x1))))
168.96/43.12	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(b(x1)))
168.96/43.12	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
168.96/43.12	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
168.96/43.12	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(a(b(b(b(x1))))))
168.96/43.12	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(b(b(x1)))))
168.96/43.12	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(b(x1))))
168.96/43.12	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(b(x1)))
168.96/43.12	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
168.96/43.12	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
168.96/43.12	    SCC Processor:
168.96/43.12	     #sccs: 1
168.96/43.12	     #rules: 3
168.96/43.12	     #arcs: 18/36
168.96/43.12	     DPs:
168.96/43.12	      b#(a(x1)) -> b#(b(b(x1)))
168.96/43.12	      b#(a(x1)) -> b#(x1)
168.96/43.12	      b#(a(x1)) -> b#(b(x1))
168.96/43.12	     TRS:
168.96/43.12	      a(x1) -> x1
168.96/43.12	      b(a(x1)) -> c(a(a(b(b(b(x1))))))
168.96/43.12	      b(x1) -> x1
168.96/43.12	      c(c(x1)) -> x1
168.96/43.12	     Arctic Interpretation Processor:
168.96/43.12	      dimension: 2
168.96/43.12	      usable rules:
168.96/43.12	       a(x1) -> x1
168.96/43.12	       b(a(x1)) -> c(a(a(b(b(b(x1))))))
168.96/43.12	       b(x1) -> x1
168.96/43.12	       c(c(x1)) -> x1
168.96/43.12	      interpretation:
168.96/43.12	       [b#](x0) = [-& 0 ]x0 + [1],
168.96/43.12	       
168.96/43.12	                 [0  0 ]     [0]
168.96/43.12	       [c](x0) = [0  -&]x0 + [1],
168.96/43.12	       
168.96/43.12	                 [0  1 ]     [0]
168.96/43.12	       [b](x0) = [-& 0 ]x0 + [0],
168.96/43.12	       
168.96/43.12	                 [0 0]     [0]
168.96/43.12	       [a](x0) = [0 1]x0 + [2]
168.96/43.12	      orientation:
168.96/43.12	       b#(a(x1)) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = b#(b(b(x1)))
168.96/43.12	       
168.96/43.12	       b#(a(x1)) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = b#(x1)
168.96/43.12	       
168.96/43.12	       b#(a(x1)) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = b#(b(x1))
168.96/43.12	       
168.96/43.12	               [0 0]     [0]           
168.96/43.12	       a(x1) = [0 1]x1 + [2] >= x1 = x1
168.96/43.12	       
168.96/43.12	                  [1 2]     [3]    [1 2]     [3]                       
168.96/43.12	       b(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = c(a(a(b(b(b(x1))))))
168.96/43.12	       
168.96/43.12	               [0  1 ]     [0]           
168.96/43.12	       b(x1) = [-& 0 ]x1 + [0] >= x1 = x1
168.96/43.12	       
168.96/43.12	                  [0 0]     [1]           
168.96/43.12	       c(c(x1)) = [0 0]x1 + [1] >= x1 = x1
168.96/43.12	      problem:
168.96/43.12	       DPs:
168.96/43.12	        
168.96/43.12	       TRS:
168.96/43.12	        a(x1) -> x1
168.96/43.12	        b(a(x1)) -> c(a(a(b(b(b(x1))))))
168.96/43.12	        b(x1) -> x1
168.96/43.12	        c(c(x1)) -> x1
168.96/43.12	      Qed
168.96/43.12	EOF