171.17/43.70	YES
171.17/43.71	
171.17/43.71	Problem:
171.17/43.71	 a(x1) -> x1
171.17/43.71	 a(b(x1)) -> b(b(a(a(c(x1)))))
171.17/43.71	 b(x1) -> x1
171.17/43.71	 c(a(c(x1))) -> x1
171.17/43.71	
171.17/43.71	Proof:
171.17/43.71	 String Reversal Processor:
171.17/43.71	  a(x1) -> x1
171.17/43.71	  b(a(x1)) -> c(a(a(b(b(x1)))))
171.17/43.71	  b(x1) -> x1
171.17/43.71	  c(a(c(x1))) -> x1
171.17/43.71	  DP Processor:
171.17/43.71	   DPs:
171.17/43.71	    b#(a(x1)) -> b#(x1)
171.17/43.71	    b#(a(x1)) -> b#(b(x1))
171.17/43.71	    b#(a(x1)) -> a#(b(b(x1)))
171.17/43.71	    b#(a(x1)) -> a#(a(b(b(x1))))
171.17/43.71	    b#(a(x1)) -> c#(a(a(b(b(x1)))))
171.17/43.71	   TRS:
171.17/43.71	    a(x1) -> x1
171.17/43.71	    b(a(x1)) -> c(a(a(b(b(x1)))))
171.17/43.71	    b(x1) -> x1
171.17/43.71	    c(a(c(x1))) -> x1
171.17/43.71	   TDG Processor:
171.17/43.71	    DPs:
171.17/43.71	     b#(a(x1)) -> b#(x1)
171.17/43.71	     b#(a(x1)) -> b#(b(x1))
171.17/43.71	     b#(a(x1)) -> a#(b(b(x1)))
171.17/43.71	     b#(a(x1)) -> a#(a(b(b(x1))))
171.17/43.71	     b#(a(x1)) -> c#(a(a(b(b(x1)))))
171.17/43.71	    TRS:
171.17/43.71	     a(x1) -> x1
171.17/43.71	     b(a(x1)) -> c(a(a(b(b(x1)))))
171.17/43.71	     b(x1) -> x1
171.17/43.71	     c(a(c(x1))) -> x1
171.17/43.71	    graph:
171.17/43.71	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
171.17/43.71	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(a(b(b(x1))))
171.17/43.71	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
171.17/43.71	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
171.17/43.71	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
171.17/43.71	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
171.17/43.71	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(b(x1))))
171.17/43.71	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
171.17/43.71	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
171.17/43.71	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
171.17/43.71	    SCC Processor:
171.17/43.71	     #sccs: 1
171.17/43.71	     #rules: 2
171.17/43.71	     #arcs: 10/25
171.17/43.71	     DPs:
171.17/43.71	      b#(a(x1)) -> b#(b(x1))
171.17/43.71	      b#(a(x1)) -> b#(x1)
171.17/43.71	     TRS:
171.17/43.71	      a(x1) -> x1
171.17/43.71	      b(a(x1)) -> c(a(a(b(b(x1)))))
171.17/43.71	      b(x1) -> x1
171.17/43.71	      c(a(c(x1))) -> x1
171.17/43.71	     Arctic Interpretation Processor:
171.17/43.71	      dimension: 2
171.17/43.71	      usable rules:
171.17/43.71	       a(x1) -> x1
171.17/43.71	       b(a(x1)) -> c(a(a(b(b(x1)))))
171.17/43.71	       b(x1) -> x1
171.17/43.71	       c(a(c(x1))) -> x1
171.17/43.71	      interpretation:
171.17/43.71	       [b#](x0) = [0 2]x0,
171.17/43.71	       
171.17/43.71	                 [1  0 ]     [0]
171.17/43.71	       [c](x0) = [0  -&]x0 + [0],
171.17/43.71	       
171.17/43.71	                 [0  1 ]     [0 ]
171.17/43.71	       [b](x0) = [-& 0 ]x0 + [-&],
171.17/43.71	       
171.17/43.71	                 [0 0]     [0]
171.17/43.71	       [a](x0) = [0 1]x0 + [0]
171.17/43.71	      orientation:
171.17/43.71	       b#(a(x1)) = [2 3]x1 + [2] >= [0 2]x1 + [0] = b#(b(x1))
171.17/43.71	       
171.17/43.71	       b#(a(x1)) = [2 3]x1 + [2] >= [0 2]x1 = b#(x1)
171.17/43.71	       
171.17/43.71	               [0 0]     [0]           
171.17/43.71	       a(x1) = [0 1]x1 + [0] >= x1 = x1
171.17/43.71	       
171.17/43.71	                  [1 2]     [1]    [1 2]     [1]                    
171.17/43.71	       b(a(x1)) = [0 1]x1 + [0] >= [0 1]x1 + [0] = c(a(a(b(b(x1)))))
171.17/43.71	       
171.17/43.71	               [0  1 ]     [0 ]           
171.17/43.71	       b(x1) = [-& 0 ]x1 + [-&] >= x1 = x1
171.17/43.71	       
171.17/43.71	                     [2 1]     [1]           
171.17/43.71	       c(a(c(x1))) = [1 0]x1 + [0] >= x1 = x1
171.17/43.71	      problem:
171.17/43.71	       DPs:
171.17/43.71	        
171.17/43.71	       TRS:
171.17/43.71	        a(x1) -> x1
171.17/43.71	        b(a(x1)) -> c(a(a(b(b(x1)))))
171.17/43.71	        b(x1) -> x1
171.17/43.71	        c(a(c(x1))) -> x1
171.17/43.71	      Qed
171.17/43.72	EOF