166.29/42.44	YES
166.29/42.44	
166.29/42.44	Problem:
166.29/42.44	 a(x1) -> x1
166.29/42.44	 a(a(x1)) -> b(x1)
166.29/42.44	 b(x1) -> c(x1)
166.29/42.44	 b(c(x1)) -> c(b(a(x1)))
166.29/42.44	 c(x1) -> x1
166.29/42.44	
166.29/42.44	Proof:
166.29/42.44	 String Reversal Processor:
166.29/42.44	  a(x1) -> x1
166.29/42.44	  a(a(x1)) -> b(x1)
166.29/42.44	  b(x1) -> c(x1)
166.29/42.44	  c(b(x1)) -> a(b(c(x1)))
166.29/42.44	  c(x1) -> x1
166.29/42.44	  DP Processor:
166.29/42.44	   DPs:
166.29/42.44	    a#(a(x1)) -> b#(x1)
166.29/42.44	    b#(x1) -> c#(x1)
166.29/42.44	    c#(b(x1)) -> c#(x1)
166.29/42.44	    c#(b(x1)) -> b#(c(x1))
166.29/42.44	    c#(b(x1)) -> a#(b(c(x1)))
166.29/42.44	   TRS:
166.29/42.44	    a(x1) -> x1
166.29/42.44	    a(a(x1)) -> b(x1)
166.29/42.44	    b(x1) -> c(x1)
166.29/42.44	    c(b(x1)) -> a(b(c(x1)))
166.29/42.44	    c(x1) -> x1
166.29/42.44	   TDG Processor:
166.29/42.44	    DPs:
166.29/42.44	     a#(a(x1)) -> b#(x1)
166.29/42.44	     b#(x1) -> c#(x1)
166.29/42.44	     c#(b(x1)) -> c#(x1)
166.29/42.44	     c#(b(x1)) -> b#(c(x1))
166.29/42.44	     c#(b(x1)) -> a#(b(c(x1)))
166.29/42.44	    TRS:
166.29/42.44	     a(x1) -> x1
166.29/42.44	     a(a(x1)) -> b(x1)
166.29/42.44	     b(x1) -> c(x1)
166.29/42.44	     c(b(x1)) -> a(b(c(x1)))
166.29/42.44	     c(x1) -> x1
166.29/42.44	    graph:
166.29/42.44	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
166.29/42.44	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
166.29/42.44	     c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
166.29/42.44	     c#(b(x1)) -> b#(c(x1)) -> b#(x1) -> c#(x1)
166.29/42.44	     c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(x1)
166.29/42.44	     b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
166.29/42.45	     b#(x1) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
166.29/42.45	     b#(x1) -> c#(x1) -> c#(b(x1)) -> c#(x1)
166.29/42.45	     a#(a(x1)) -> b#(x1) -> b#(x1) -> c#(x1)
166.29/42.45	    Arctic Interpretation Processor:
166.29/42.45	     dimension: 2
166.29/42.45	     usable rules:
166.29/42.45	      a(x1) -> x1
166.29/42.45	      a(a(x1)) -> b(x1)
166.29/42.45	      b(x1) -> c(x1)
166.29/42.45	      c(b(x1)) -> a(b(c(x1)))
166.29/42.45	      c(x1) -> x1
166.29/42.45	     interpretation:
166.29/42.45	      [c#](x0) = [-& 0 ]x0 + [0],
166.29/42.45	      
166.29/42.45	      [b#](x0) = [0 0]x0 + [0],
166.29/42.45	      
166.29/42.45	      [a#](x0) = [1  -&]x0 + [0],
166.29/42.45	      
166.29/42.45	                [0 0]  
166.29/42.45	      [c](x0) = [0 0]x0,
166.29/42.45	      
166.29/42.45	                [0 0]     [-&]
166.29/42.45	      [b](x0) = [1 1]x0 + [1 ],
166.29/42.45	      
166.29/42.45	                [0 0]     [1]
166.29/42.45	      [a](x0) = [1 0]x0 + [0]
166.29/42.45	     orientation:
166.29/42.45	      a#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [0] = b#(x1)
166.29/42.45	      
166.29/42.45	      b#(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = c#(x1)
166.29/42.45	      
166.29/42.45	      c#(b(x1)) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = c#(x1)
166.29/42.45	      
166.29/42.45	      c#(b(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(c(x1))
166.29/42.45	      
166.29/42.45	      c#(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [0] = a#(b(c(x1)))
166.29/42.45	      
166.29/42.45	              [0 0]     [1]           
166.29/42.45	      a(x1) = [1 0]x1 + [0] >= x1 = x1
166.29/42.45	      
166.29/42.45	                 [1 0]     [1]    [0 0]     [-&]        
166.29/42.45	      a(a(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [1 ] = b(x1)
166.29/42.45	      
166.29/42.45	              [0 0]     [-&]    [0 0]          
166.29/42.45	      b(x1) = [1 1]x1 + [1 ] >= [0 0]x1 = c(x1)
166.29/42.45	      
166.29/42.45	                 [1 1]     [1]    [1 1]     [1]              
166.29/42.45	      c(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(c(x1)))
166.29/42.45	      
166.29/42.45	              [0 0]             
166.29/42.45	      c(x1) = [0 0]x1 >= x1 = x1
166.29/42.45	     problem:
166.29/42.45	      DPs:
166.29/42.45	       b#(x1) -> c#(x1)
166.29/42.45	       c#(b(x1)) -> a#(b(c(x1)))
166.29/42.45	      TRS:
166.29/42.45	       a(x1) -> x1
166.29/42.45	       a(a(x1)) -> b(x1)
166.29/42.45	       b(x1) -> c(x1)
166.29/42.45	       c(b(x1)) -> a(b(c(x1)))
166.29/42.45	       c(x1) -> x1
166.29/42.45	     Restore Modifier:
166.29/42.45	      DPs:
166.29/42.45	       b#(x1) -> c#(x1)
166.29/42.45	       c#(b(x1)) -> a#(b(c(x1)))
166.29/42.45	      TRS:
166.29/42.45	       a(x1) -> x1
166.29/42.45	       a(a(x1)) -> b(x1)
166.29/42.45	       b(x1) -> c(x1)
166.29/42.45	       c(b(x1)) -> a(b(c(x1)))
166.29/42.45	       c(x1) -> x1
166.29/42.45	      EDG Processor:
166.29/42.45	       DPs:
166.29/42.45	        b#(x1) -> c#(x1)
166.29/42.45	        c#(b(x1)) -> a#(b(c(x1)))
166.29/42.45	       TRS:
166.29/42.45	        a(x1) -> x1
166.29/42.45	        a(a(x1)) -> b(x1)
166.29/42.45	        b(x1) -> c(x1)
166.29/42.45	        c(b(x1)) -> a(b(c(x1)))
166.29/42.45	        c(x1) -> x1
166.29/42.45	       graph:
166.29/42.45	        b#(x1) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
166.29/42.45	       SCC Processor:
166.29/42.45	        #sccs: 0
166.29/42.45	        #rules: 0
166.29/42.45	        #arcs: 1/4
166.29/42.45	        
166.29/42.45	EOF