165.80/42.21	YES
165.80/42.21	
165.80/42.21	Problem:
165.80/42.21	 a(x1) -> x1
165.80/42.21	 a(b(x1)) -> b(b(a(c(x1))))
165.80/42.21	 b(b(x1)) -> x1
165.80/42.21	 c(c(x1)) -> a(x1)
165.80/42.21	
165.80/42.21	Proof:
165.80/42.21	 String Reversal Processor:
165.80/42.21	  a(x1) -> x1
165.80/42.21	  b(a(x1)) -> c(a(b(b(x1))))
165.80/42.21	  b(b(x1)) -> x1
165.80/42.21	  c(c(x1)) -> a(x1)
165.80/42.21	  DP Processor:
165.80/42.21	   DPs:
165.80/42.21	    b#(a(x1)) -> b#(x1)
165.80/42.21	    b#(a(x1)) -> b#(b(x1))
165.80/42.21	    b#(a(x1)) -> a#(b(b(x1)))
165.80/42.21	    b#(a(x1)) -> c#(a(b(b(x1))))
165.80/42.21	    c#(c(x1)) -> a#(x1)
165.80/42.21	   TRS:
165.80/42.21	    a(x1) -> x1
165.80/42.21	    b(a(x1)) -> c(a(b(b(x1))))
165.80/42.21	    b(b(x1)) -> x1
165.80/42.21	    c(c(x1)) -> a(x1)
165.80/42.21	   TDG Processor:
165.80/42.21	    DPs:
165.80/42.21	     b#(a(x1)) -> b#(x1)
165.80/42.21	     b#(a(x1)) -> b#(b(x1))
165.80/42.21	     b#(a(x1)) -> a#(b(b(x1)))
165.80/42.21	     b#(a(x1)) -> c#(a(b(b(x1))))
165.80/42.21	     c#(c(x1)) -> a#(x1)
165.80/42.21	    TRS:
165.80/42.21	     a(x1) -> x1
165.80/42.21	     b(a(x1)) -> c(a(b(b(x1))))
165.80/42.21	     b(b(x1)) -> x1
165.80/42.21	     c(c(x1)) -> a(x1)
165.80/42.21	    graph:
165.80/42.21	     b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(c(x1)) -> a#(x1)
165.80/42.21	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(b(x1))))
165.80/42.21	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
165.80/42.21	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
165.80/42.21	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
165.80/42.21	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
165.80/42.21	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
165.80/42.21	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
165.80/42.21	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
165.80/42.21	    SCC Processor:
165.80/42.21	     #sccs: 1
165.80/42.21	     #rules: 2
165.80/42.21	     #arcs: 9/25
165.80/42.21	     DPs:
165.80/42.21	      b#(a(x1)) -> b#(b(x1))
165.80/42.21	      b#(a(x1)) -> b#(x1)
165.80/42.21	     TRS:
165.80/42.21	      a(x1) -> x1
165.80/42.21	      b(a(x1)) -> c(a(b(b(x1))))
165.80/42.21	      b(b(x1)) -> x1
165.80/42.21	      c(c(x1)) -> a(x1)
165.80/42.21	     Arctic Interpretation Processor:
165.80/42.21	      dimension: 2
165.80/42.21	      usable rules:
165.80/42.21	       a(x1) -> x1
165.80/42.21	       b(a(x1)) -> c(a(b(b(x1))))
165.80/42.21	       b(b(x1)) -> x1
165.80/42.21	       c(c(x1)) -> a(x1)
165.80/42.21	      interpretation:
165.80/42.21	       [b#](x0) = [1 0]x0,
165.80/42.21	       
165.80/42.21	                 [0 0]  
165.80/42.21	       [c](x0) = [1 1]x0,
165.80/42.21	       
165.80/42.21	                 [0  -&]  
165.80/42.21	       [b](x0) = [1  0 ]x0,
165.80/42.21	       
165.80/42.21	                 [1  0 ]  
165.80/42.21	       [a](x0) = [-& 0 ]x0
165.80/42.21	      orientation:
165.80/42.21	       b#(a(x1)) = [2 1]x1 >= [1 0]x1 = b#(b(x1))
165.80/42.21	       
165.80/42.21	       b#(a(x1)) = [2 1]x1 >= [1 0]x1 = b#(x1)
165.80/42.21	       
165.80/42.21	               [1  0 ]             
165.80/42.21	       a(x1) = [-& 0 ]x1 >= x1 = x1
165.80/42.21	       
165.80/42.21	                  [1 0]      [1 0]                   
165.80/42.21	       b(a(x1)) = [2 1]x1 >= [2 1]x1 = c(a(b(b(x1))))
165.80/42.21	       
165.80/42.21	                  [0  -&]             
165.80/42.21	       b(b(x1)) = [1  0 ]x1 >= x1 = x1
165.80/42.21	       
165.80/42.21	                  [1 1]      [1  0 ]          
165.80/42.21	       c(c(x1)) = [2 2]x1 >= [-& 0 ]x1 = a(x1)
165.80/42.21	      problem:
165.80/42.21	       DPs:
165.80/42.21	        
165.80/42.21	       TRS:
165.80/42.21	        a(x1) -> x1
165.80/42.21	        b(a(x1)) -> c(a(b(b(x1))))
165.80/42.21	        b(b(x1)) -> x1
165.80/42.21	        c(c(x1)) -> a(x1)
165.80/42.21	      Qed
165.80/42.22	EOF