168.20/43.00	YES
168.20/43.01	
168.20/43.01	Problem:
168.20/43.01	 a(x1) -> x1
168.20/43.01	 a(b(x1)) -> b(b(a(c(x1))))
168.20/43.01	 b(b(x1)) -> a(x1)
168.20/43.01	 c(c(x1)) -> x1
168.20/43.01	
168.20/43.01	Proof:
168.20/43.01	 String Reversal Processor:
168.20/43.01	  a(x1) -> x1
168.20/43.01	  b(a(x1)) -> c(a(b(b(x1))))
168.20/43.01	  b(b(x1)) -> a(x1)
168.20/43.01	  c(c(x1)) -> x1
168.20/43.01	  DP Processor:
168.20/43.01	   DPs:
168.20/43.01	    b#(a(x1)) -> b#(x1)
168.20/43.01	    b#(a(x1)) -> b#(b(x1))
168.20/43.01	    b#(a(x1)) -> a#(b(b(x1)))
168.20/43.01	    b#(a(x1)) -> c#(a(b(b(x1))))
168.20/43.01	    b#(b(x1)) -> a#(x1)
168.20/43.01	   TRS:
168.20/43.01	    a(x1) -> x1
168.20/43.01	    b(a(x1)) -> c(a(b(b(x1))))
168.20/43.01	    b(b(x1)) -> a(x1)
168.20/43.01	    c(c(x1)) -> x1
168.20/43.01	   TDG Processor:
168.20/43.01	    DPs:
168.20/43.01	     b#(a(x1)) -> b#(x1)
168.20/43.01	     b#(a(x1)) -> b#(b(x1))
168.20/43.01	     b#(a(x1)) -> a#(b(b(x1)))
168.20/43.01	     b#(a(x1)) -> c#(a(b(b(x1))))
168.20/43.01	     b#(b(x1)) -> a#(x1)
168.20/43.01	    TRS:
168.20/43.01	     a(x1) -> x1
168.20/43.01	     b(a(x1)) -> c(a(b(b(x1))))
168.20/43.01	     b(b(x1)) -> a(x1)
168.20/43.01	     c(c(x1)) -> x1
168.20/43.01	    graph:
168.20/43.01	     b#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> a#(x1)
168.20/43.01	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(b(x1))))
168.20/43.01	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
168.20/43.01	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
168.20/43.01	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
168.20/43.01	     b#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
168.20/43.01	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
168.20/43.01	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
168.20/43.01	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
168.20/43.01	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
168.20/43.01	    SCC Processor:
168.20/43.01	     #sccs: 1
168.20/43.01	     #rules: 2
168.20/43.01	     #arcs: 10/25
168.20/43.01	     DPs:
168.20/43.01	      b#(a(x1)) -> b#(b(x1))
168.20/43.01	      b#(a(x1)) -> b#(x1)
168.20/43.01	     TRS:
168.20/43.01	      a(x1) -> x1
168.20/43.01	      b(a(x1)) -> c(a(b(b(x1))))
168.20/43.01	      b(b(x1)) -> a(x1)
168.20/43.01	      c(c(x1)) -> x1
168.20/43.01	     Arctic Interpretation Processor:
168.20/43.01	      dimension: 2
168.20/43.01	      usable rules:
168.20/43.01	       a(x1) -> x1
168.20/43.01	       b(a(x1)) -> c(a(b(b(x1))))
168.20/43.01	       b(b(x1)) -> a(x1)
168.20/43.01	       c(c(x1)) -> x1
168.20/43.01	      interpretation:
168.20/43.01	       [b#](x0) = [0 1]x0,
168.20/43.01	       
168.20/43.01	                 [1  0 ]  
168.20/43.01	       [c](x0) = [0  -&]x0,
168.20/43.01	       
168.20/43.01	                 [0 2]  
168.20/43.01	       [b](x0) = [0 1]x0,
168.20/43.01	       
168.20/43.01	                 [0 1]  
168.20/43.01	       [a](x0) = [1 2]x0
168.20/43.01	      orientation:
168.20/43.01	       b#(a(x1)) = [2 3]x1 >= [1 2]x1 = b#(b(x1))
168.20/43.01	       
168.20/43.01	       b#(a(x1)) = [2 3]x1 >= [0 1]x1 = b#(x1)
168.20/43.01	       
168.20/43.01	               [0 1]             
168.20/43.01	       a(x1) = [1 2]x1 >= x1 = x1
168.20/43.01	       
168.20/43.01	                  [3 4]      [3 4]                   
168.20/43.01	       b(a(x1)) = [2 3]x1 >= [2 3]x1 = c(a(b(b(x1))))
168.20/43.01	       
168.20/43.01	                  [2 3]      [0 1]          
168.20/43.01	       b(b(x1)) = [1 2]x1 >= [1 2]x1 = a(x1)
168.20/43.01	       
168.20/43.01	                  [2 1]             
168.20/43.01	       c(c(x1)) = [1 0]x1 >= x1 = x1
168.20/43.01	      problem:
168.20/43.01	       DPs:
168.20/43.01	        
168.20/43.01	       TRS:
168.20/43.01	        a(x1) -> x1
168.20/43.01	        b(a(x1)) -> c(a(b(b(x1))))
168.20/43.01	        b(b(x1)) -> a(x1)
168.20/43.01	        c(c(x1)) -> x1
168.20/43.01	      Qed
168.20/43.01	EOF