164.30/42.00	YES
164.30/42.01	
164.30/42.01	Problem:
164.30/42.01	 a(x1) -> x1
164.30/42.01	 a(a(x1)) -> b(x1)
164.30/42.01	 b(x1) -> x1
164.30/42.01	 b(c(x1)) -> c(c(b(a(x1))))
164.30/42.01	 c(x1) -> x1
164.30/42.01	
164.30/42.01	Proof:
164.30/42.01	 String Reversal Processor:
164.30/42.01	  a(x1) -> x1
164.30/42.01	  a(a(x1)) -> b(x1)
164.30/42.01	  b(x1) -> x1
164.30/42.01	  c(b(x1)) -> a(b(c(c(x1))))
164.30/42.01	  c(x1) -> x1
164.30/42.01	  DP Processor:
164.30/42.01	   DPs:
164.30/42.01	    a#(a(x1)) -> b#(x1)
164.30/42.01	    c#(b(x1)) -> c#(x1)
164.30/42.01	    c#(b(x1)) -> c#(c(x1))
164.30/42.01	    c#(b(x1)) -> b#(c(c(x1)))
164.30/42.01	    c#(b(x1)) -> a#(b(c(c(x1))))
164.30/42.01	   TRS:
164.30/42.01	    a(x1) -> x1
164.30/42.01	    a(a(x1)) -> b(x1)
164.30/42.01	    b(x1) -> x1
164.30/42.01	    c(b(x1)) -> a(b(c(c(x1))))
164.30/42.01	    c(x1) -> x1
164.30/42.01	   TDG Processor:
164.30/42.01	    DPs:
164.30/42.01	     a#(a(x1)) -> b#(x1)
164.30/42.01	     c#(b(x1)) -> c#(x1)
164.30/42.01	     c#(b(x1)) -> c#(c(x1))
164.30/42.01	     c#(b(x1)) -> b#(c(c(x1)))
164.30/42.01	     c#(b(x1)) -> a#(b(c(c(x1))))
164.30/42.01	    TRS:
164.30/42.01	     a(x1) -> x1
164.30/42.01	     a(a(x1)) -> b(x1)
164.30/42.01	     b(x1) -> x1
164.30/42.01	     c(b(x1)) -> a(b(c(c(x1))))
164.30/42.01	     c(x1) -> x1
164.30/42.01	    graph:
164.30/42.01	     c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(b(c(c(x1))))
164.30/42.01	     c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> b#(c(c(x1)))
164.30/42.01	     c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1))
164.30/42.01	     c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(x1)
164.30/42.01	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(c(x1))))
164.30/42.01	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(c(x1)))
164.30/42.01	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(c(x1))
164.30/42.01	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
164.30/42.01	     c#(b(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> b#(x1)
164.30/42.01	    SCC Processor:
164.30/42.01	     #sccs: 1
164.30/42.01	     #rules: 2
164.30/42.01	     #arcs: 9/25
164.30/42.01	     DPs:
164.30/42.01	      c#(b(x1)) -> c#(c(x1))
164.30/42.01	      c#(b(x1)) -> c#(x1)
164.30/42.01	     TRS:
164.30/42.01	      a(x1) -> x1
164.30/42.01	      a(a(x1)) -> b(x1)
164.30/42.01	      b(x1) -> x1
164.30/42.01	      c(b(x1)) -> a(b(c(c(x1))))
164.30/42.01	      c(x1) -> x1
164.30/42.01	     Arctic Interpretation Processor:
164.30/42.01	      dimension: 2
164.30/42.01	      usable rules:
164.30/42.01	       a(x1) -> x1
164.30/42.01	       a(a(x1)) -> b(x1)
164.30/42.01	       b(x1) -> x1
164.30/42.01	       c(b(x1)) -> a(b(c(c(x1))))
164.30/42.01	       c(x1) -> x1
164.30/42.01	      interpretation:
164.30/42.01	       [c#](x0) = [-& 0 ]x0 + [0],
164.30/42.01	       
164.30/42.01	                 [0 0]     [0]
164.30/42.01	       [c](x0) = [0 0]x0 + [2],
164.30/42.01	       
164.30/42.01	                 [0 0]     [-&]
164.30/42.01	       [b](x0) = [1 1]x0 + [3 ],
164.30/42.01	       
164.30/42.01	                 [0 0]     [3 ]
164.30/42.01	       [a](x0) = [1 0]x0 + [-&]
164.30/42.01	      orientation:
164.30/42.01	       c#(b(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [2] = c#(c(x1))
164.30/42.01	       
164.30/42.01	       c#(b(x1)) = [1 1]x1 + [3] >= [-& 0 ]x1 + [0] = c#(x1)
164.30/42.01	       
164.30/42.01	               [0 0]     [3 ]           
164.30/42.01	       a(x1) = [1 0]x1 + [-&] >= x1 = x1
164.30/42.01	       
164.30/42.01	                  [1 0]     [3]    [0 0]     [-&]        
164.30/42.01	       a(a(x1)) = [1 1]x1 + [4] >= [1 1]x1 + [3 ] = b(x1)
164.30/42.01	       
164.30/42.01	               [0 0]     [-&]           
164.30/42.01	       b(x1) = [1 1]x1 + [3 ] >= x1 = x1
164.30/42.01	       
164.30/42.01	                  [1 1]     [3]    [1 1]     [3]                 
164.30/42.01	       c(b(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = a(b(c(c(x1))))
164.30/42.01	       
164.30/42.01	               [0 0]     [0]           
164.30/42.01	       c(x1) = [0 0]x1 + [2] >= x1 = x1
164.30/42.01	      problem:
164.30/42.01	       DPs:
164.30/42.01	        
164.30/42.01	       TRS:
164.30/42.01	        a(x1) -> x1
164.30/42.01	        a(a(x1)) -> b(x1)
164.30/42.01	        b(x1) -> x1
164.30/42.01	        c(b(x1)) -> a(b(c(c(x1))))
164.30/42.01	        c(x1) -> x1
164.30/42.01	      Qed
164.30/42.02	EOF