166.50/42.64	YES
166.50/42.64	
166.50/42.64	Problem:
166.50/42.64	 a(x1) -> x1
166.50/42.64	 a(b(x1)) -> b(b(b(a(c(x1)))))
166.50/42.64	 b(x1) -> x1
166.50/42.64	 c(c(x1)) -> a(x1)
166.50/42.64	
166.50/42.64	Proof:
166.50/42.64	 String Reversal Processor:
166.50/42.64	  a(x1) -> x1
166.50/42.64	  b(a(x1)) -> c(a(b(b(b(x1)))))
166.50/42.64	  b(x1) -> x1
166.50/42.64	  c(c(x1)) -> a(x1)
166.50/42.64	  DP Processor:
166.50/42.64	   DPs:
166.50/42.64	    b#(a(x1)) -> b#(x1)
166.50/42.64	    b#(a(x1)) -> b#(b(x1))
166.50/42.64	    b#(a(x1)) -> b#(b(b(x1)))
166.50/42.64	    b#(a(x1)) -> a#(b(b(b(x1))))
166.50/42.64	    b#(a(x1)) -> c#(a(b(b(b(x1)))))
166.50/42.64	    c#(c(x1)) -> a#(x1)
166.50/42.64	   TRS:
166.50/42.64	    a(x1) -> x1
166.50/42.64	    b(a(x1)) -> c(a(b(b(b(x1)))))
166.50/42.64	    b(x1) -> x1
166.50/42.64	    c(c(x1)) -> a(x1)
166.50/42.64	   TDG Processor:
166.50/42.64	    DPs:
166.50/42.64	     b#(a(x1)) -> b#(x1)
166.50/42.64	     b#(a(x1)) -> b#(b(x1))
166.50/42.64	     b#(a(x1)) -> b#(b(b(x1)))
166.50/42.64	     b#(a(x1)) -> a#(b(b(b(x1))))
166.50/42.64	     b#(a(x1)) -> c#(a(b(b(b(x1)))))
166.50/42.64	     c#(c(x1)) -> a#(x1)
166.50/42.64	    TRS:
166.50/42.64	     a(x1) -> x1
166.50/42.64	     b(a(x1)) -> c(a(b(b(b(x1)))))
166.50/42.64	     b(x1) -> x1
166.50/42.64	     c(c(x1)) -> a(x1)
166.50/42.64	    graph:
166.50/42.64	     b#(a(x1)) -> c#(a(b(b(b(x1))))) -> c#(c(x1)) -> a#(x1)
166.50/42.64	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> c#(a(b(b(b(x1)))))
166.50/42.64	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> a#(b(b(b(x1))))
166.50/42.64	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(b(b(x1)))
166.50/42.64	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(b(x1))
166.50/42.64	     b#(a(x1)) -> b#(b(b(x1))) -> b#(a(x1)) -> b#(x1)
166.50/42.64	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(b(b(x1)))))
166.50/42.64	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(b(x1))))
166.50/42.64	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(b(x1)))
166.50/42.64	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
166.50/42.64	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
166.50/42.64	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(b(x1)))))
166.50/42.64	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(b(x1))))
166.50/42.64	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(b(x1)))
166.50/42.64	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
166.50/42.64	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
166.50/42.64	    SCC Processor:
166.50/42.64	     #sccs: 1
166.50/42.64	     #rules: 3
166.50/42.64	     #arcs: 16/36
166.50/42.64	     DPs:
166.50/42.64	      b#(a(x1)) -> b#(b(b(x1)))
166.50/42.64	      b#(a(x1)) -> b#(x1)
166.50/42.64	      b#(a(x1)) -> b#(b(x1))
166.50/42.64	     TRS:
166.50/42.64	      a(x1) -> x1
166.50/42.64	      b(a(x1)) -> c(a(b(b(b(x1)))))
166.50/42.64	      b(x1) -> x1
166.50/42.64	      c(c(x1)) -> a(x1)
166.50/42.64	     Arctic Interpretation Processor:
166.50/42.64	      dimension: 2
166.50/42.64	      usable rules:
166.50/42.64	       a(x1) -> x1
166.50/42.64	       b(a(x1)) -> c(a(b(b(b(x1)))))
166.50/42.64	       b(x1) -> x1
166.50/42.64	       c(c(x1)) -> a(x1)
166.50/42.64	      interpretation:
166.50/42.64	       [b#](x0) = [0 0]x0 + [0],
166.50/42.64	       
166.50/42.64	                 [-& 0 ]     [0 ]
166.50/42.64	       [c](x0) = [2  0 ]x0 + [-&],
166.50/42.64	       
166.50/42.64	                 [0  0 ]     [0]
166.50/42.64	       [b](x0) = [-& 0 ]x0 + [0],
166.50/42.64	       
166.50/42.64	                 [0  -&]     [0]
166.50/42.64	       [a](x0) = [2  2 ]x0 + [2]
166.50/42.64	      orientation:
166.50/42.64	       b#(a(x1)) = [2 2]x1 + [2] >= [0 0]x1 + [0] = b#(b(b(x1)))
166.50/42.64	       
166.50/42.64	       b#(a(x1)) = [2 2]x1 + [2] >= [0 0]x1 + [0] = b#(x1)
166.50/42.64	       
166.50/42.64	       b#(a(x1)) = [2 2]x1 + [2] >= [0 0]x1 + [0] = b#(b(x1))
166.50/42.64	       
166.50/42.64	               [0  -&]     [0]           
166.50/42.64	       a(x1) = [2  2 ]x1 + [2] >= x1 = x1
166.50/42.64	       
166.50/42.64	                  [2 2]     [2]    [2 2]     [2]                    
166.50/42.64	       b(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = c(a(b(b(b(x1)))))
166.50/42.64	       
166.50/42.64	               [0  0 ]     [0]           
166.50/42.64	       b(x1) = [-& 0 ]x1 + [0] >= x1 = x1
166.50/42.64	       
166.50/42.64	                  [2 0]     [0]    [0  -&]     [0]        
166.50/42.64	       c(c(x1)) = [2 2]x1 + [2] >= [2  2 ]x1 + [2] = a(x1)
166.50/42.64	      problem:
166.50/42.64	       DPs:
166.50/42.64	        
166.50/42.64	       TRS:
166.50/42.64	        a(x1) -> x1
166.50/42.64	        b(a(x1)) -> c(a(b(b(b(x1)))))
166.50/42.64	        b(x1) -> x1
166.50/42.64	        c(c(x1)) -> a(x1)
166.50/42.64	      Qed
166.50/42.65	EOF