168.10/44.46	YES
168.10/44.46	
168.10/44.46	Problem:
168.10/44.46	 a(x1) -> x1
168.10/44.46	 a(a(b(x1))) -> b(b(a(a(x1))))
168.10/44.46	 c(b(x1)) -> c(a(x1))
168.10/44.46	
168.10/44.46	Proof:
168.10/44.46	 String Reversal Processor:
168.10/44.46	  a(x1) -> x1
168.10/44.46	  b(a(a(x1))) -> a(a(b(b(x1))))
168.10/44.46	  b(c(x1)) -> a(c(x1))
168.10/44.46	  DP Processor:
168.10/44.46	   DPs:
168.10/44.46	    b#(a(a(x1))) -> b#(x1)
168.10/44.46	    b#(a(a(x1))) -> b#(b(x1))
168.10/44.46	    b#(a(a(x1))) -> a#(b(b(x1)))
168.10/44.46	    b#(a(a(x1))) -> a#(a(b(b(x1))))
168.10/44.46	    b#(c(x1)) -> a#(c(x1))
168.10/44.46	   TRS:
168.10/44.46	    a(x1) -> x1
168.10/44.46	    b(a(a(x1))) -> a(a(b(b(x1))))
168.10/44.46	    b(c(x1)) -> a(c(x1))
168.10/44.46	   TDG Processor:
168.10/44.46	    DPs:
168.10/44.46	     b#(a(a(x1))) -> b#(x1)
168.10/44.46	     b#(a(a(x1))) -> b#(b(x1))
168.10/44.46	     b#(a(a(x1))) -> a#(b(b(x1)))
168.10/44.46	     b#(a(a(x1))) -> a#(a(b(b(x1))))
168.10/44.46	     b#(c(x1)) -> a#(c(x1))
168.10/44.46	    TRS:
168.10/44.46	     a(x1) -> x1
168.10/44.46	     b(a(a(x1))) -> a(a(b(b(x1))))
168.10/44.46	     b(c(x1)) -> a(c(x1))
168.10/44.46	    graph:
168.10/44.46	     b#(a(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(c(x1))
168.10/44.46	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(b(b(x1))))
168.10/44.46	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(b(b(x1)))
168.10/44.46	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
168.10/44.46	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1)
168.10/44.46	     b#(a(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(c(x1))
168.10/44.46	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(b(x1))))
168.10/44.46	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(b(x1)))
168.10/44.46	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1))
168.10/44.46	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
168.10/44.46	    SCC Processor:
168.10/44.46	     #sccs: 1
168.10/44.46	     #rules: 2
168.10/44.46	     #arcs: 10/25
168.10/44.46	     DPs:
168.10/44.46	      b#(a(a(x1))) -> b#(b(x1))
168.10/44.46	      b#(a(a(x1))) -> b#(x1)
168.10/44.46	     TRS:
168.10/44.46	      a(x1) -> x1
168.10/44.46	      b(a(a(x1))) -> a(a(b(b(x1))))
168.10/44.46	      b(c(x1)) -> a(c(x1))
168.10/44.46	     Arctic Interpretation Processor:
168.10/44.46	      dimension: 2
168.10/44.46	      usable rules:
168.10/44.46	       a(x1) -> x1
168.10/44.46	       b(a(a(x1))) -> a(a(b(b(x1))))
168.10/44.46	       b(c(x1)) -> a(c(x1))
168.10/44.46	      interpretation:
168.10/44.46	       [b#](x0) = [0  -&]x0,
168.10/44.46	       
168.10/44.46	                 [-& 2 ]     [3]
168.10/44.46	       [c](x0) = [-& 1 ]x0 + [2],
168.10/44.46	       
168.10/44.46	                 [0 0]     [-&]
168.10/44.46	       [b](x0) = [0 0]x0 + [0 ],
168.10/44.46	       
168.10/44.46	                 [0 1]     [1]
168.10/44.46	       [a](x0) = [0 0]x0 + [0]
168.10/44.46	      orientation:
168.10/44.46	       b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 = b#(b(x1))
168.10/44.46	       
168.10/44.46	       b#(a(a(x1))) = [1 1]x1 + [1] >= [0  -&]x1 = b#(x1)
168.10/44.46	       
168.10/44.46	               [0 1]     [1]           
168.10/44.46	       a(x1) = [0 0]x1 + [0] >= x1 = x1
168.10/44.46	       
168.10/44.46	                     [1 1]     [1]    [1 1]     [1]                 
168.10/44.46	       b(a(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(a(b(b(x1))))
168.10/44.46	       
168.10/44.46	                  [-& 2 ]     [3]    [-& 2 ]     [3]           
168.10/44.46	       b(c(x1)) = [-& 2 ]x1 + [3] >= [-& 2 ]x1 + [3] = a(c(x1))
168.10/44.46	      problem:
168.10/44.46	       DPs:
168.10/44.46	        
168.10/44.46	       TRS:
168.10/44.46	        a(x1) -> x1
168.10/44.46	        b(a(a(x1))) -> a(a(b(b(x1))))
168.10/44.46	        b(c(x1)) -> a(c(x1))
168.10/44.46	      Qed
168.10/44.47	EOF