168.48/42.98	YES
168.48/42.99	
168.48/42.99	Problem:
168.48/42.99	 a(x1) -> x1
168.48/42.99	 a(b(x1)) -> b(b(a(a(c(x1)))))
168.48/42.99	 b(x1) -> x1
168.48/42.99	 c(c(x1)) -> x1
168.48/42.99	
168.48/42.99	Proof:
168.48/42.99	 String Reversal Processor:
168.48/42.99	  a(x1) -> x1
168.48/42.99	  b(a(x1)) -> c(a(a(b(b(x1)))))
168.48/42.99	  b(x1) -> x1
168.48/42.99	  c(c(x1)) -> x1
168.48/42.99	  DP Processor:
168.48/42.99	   DPs:
168.48/42.99	    b#(a(x1)) -> b#(x1)
168.48/42.99	    b#(a(x1)) -> b#(b(x1))
168.48/42.99	    b#(a(x1)) -> a#(b(b(x1)))
168.48/42.99	    b#(a(x1)) -> a#(a(b(b(x1))))
168.48/42.99	    b#(a(x1)) -> c#(a(a(b(b(x1)))))
168.48/42.99	   TRS:
168.48/42.99	    a(x1) -> x1
168.48/42.99	    b(a(x1)) -> c(a(a(b(b(x1)))))
168.48/42.99	    b(x1) -> x1
168.48/42.99	    c(c(x1)) -> x1
168.48/42.99	   TDG Processor:
168.48/42.99	    DPs:
168.48/42.99	     b#(a(x1)) -> b#(x1)
168.48/42.99	     b#(a(x1)) -> b#(b(x1))
168.48/42.99	     b#(a(x1)) -> a#(b(b(x1)))
168.48/42.99	     b#(a(x1)) -> a#(a(b(b(x1))))
168.48/42.99	     b#(a(x1)) -> c#(a(a(b(b(x1)))))
168.48/42.99	    TRS:
168.48/42.99	     a(x1) -> x1
168.48/42.99	     b(a(x1)) -> c(a(a(b(b(x1)))))
168.48/42.99	     b(x1) -> x1
168.48/42.99	     c(c(x1)) -> x1
168.48/42.99	    graph:
168.48/42.99	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
168.48/42.99	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(a(b(b(x1))))
168.48/42.99	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
168.48/42.99	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
168.48/42.99	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
168.48/42.99	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
168.48/42.99	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(b(x1))))
168.48/42.99	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
168.48/42.99	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
168.48/42.99	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
168.48/42.99	    SCC Processor:
168.48/42.99	     #sccs: 1
168.48/42.99	     #rules: 2
168.48/42.99	     #arcs: 10/25
168.48/42.99	     DPs:
168.48/42.99	      b#(a(x1)) -> b#(b(x1))
168.48/42.99	      b#(a(x1)) -> b#(x1)
168.48/42.99	     TRS:
168.48/42.99	      a(x1) -> x1
168.48/42.99	      b(a(x1)) -> c(a(a(b(b(x1)))))
168.48/42.99	      b(x1) -> x1
168.48/42.99	      c(c(x1)) -> x1
168.48/42.99	     Arctic Interpretation Processor:
168.48/42.99	      dimension: 2
168.48/42.99	      usable rules:
168.48/42.99	       a(x1) -> x1
168.48/42.99	       b(a(x1)) -> c(a(a(b(b(x1)))))
168.48/42.99	       b(x1) -> x1
168.48/42.99	       c(c(x1)) -> x1
168.48/42.99	      interpretation:
168.48/42.99	       [b#](x0) = [1 0]x0 + [2],
168.48/42.99	       
168.48/42.99	                 [-& 0 ]     [3 ]
168.48/42.99	       [c](x0) = [0  1 ]x0 + [-&],
168.48/42.99	       
168.48/42.99	                 [0  -&]     [0]
168.48/42.99	       [b](x0) = [1  0 ]x0 + [1],
168.48/42.99	       
168.48/42.99	                 [1 0]     [3]
168.48/42.99	       [a](x0) = [0 0]x0 + [0]
168.48/42.99	      orientation:
168.48/42.99	       b#(a(x1)) = [2 1]x1 + [4] >= [1 0]x1 + [2] = b#(b(x1))
168.48/42.99	       
168.48/42.99	       b#(a(x1)) = [2 1]x1 + [4] >= [1 0]x1 + [2] = b#(x1)
168.48/42.99	       
168.48/42.99	               [1 0]     [3]           
168.48/42.99	       a(x1) = [0 0]x1 + [0] >= x1 = x1
168.48/42.99	       
168.48/42.99	                  [1 0]     [3]    [1 0]     [3]                    
168.48/42.99	       b(a(x1)) = [2 1]x1 + [4] >= [2 1]x1 + [4] = c(a(a(b(b(x1)))))
168.48/42.99	       
168.48/42.99	               [0  -&]     [0]           
168.48/42.99	       b(x1) = [1  0 ]x1 + [1] >= x1 = x1
168.48/42.99	       
168.48/42.99	                  [0 1]     [3]           
168.48/42.99	       c(c(x1)) = [1 2]x1 + [3] >= x1 = x1
168.48/42.99	      problem:
168.48/42.99	       DPs:
168.48/42.99	        
168.48/42.99	       TRS:
168.48/42.99	        a(x1) -> x1
168.48/42.99	        b(a(x1)) -> c(a(a(b(b(x1)))))
168.48/42.99	        b(x1) -> x1
168.48/42.99	        c(c(x1)) -> x1
168.48/42.99	      Qed
168.48/42.99	EOF