171.06/43.83	YES
171.06/43.84	
171.06/43.84	Problem:
171.06/43.84	 a(x1) -> b(x1)
171.06/43.84	 a(b(b(x1))) -> c(x1)
171.06/43.84	 a(c(x1)) -> c(b(a(a(x1))))
171.06/43.84	
171.06/43.84	Proof:
171.06/43.84	 String Reversal Processor:
171.06/43.84	  a(x1) -> b(x1)
171.06/43.84	  b(b(a(x1))) -> c(x1)
171.06/43.84	  c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	  DP Processor:
171.06/43.84	   DPs:
171.06/43.84	    a#(x1) -> b#(x1)
171.06/43.84	    b#(b(a(x1))) -> c#(x1)
171.06/43.84	    c#(a(x1)) -> c#(x1)
171.06/43.84	    c#(a(x1)) -> b#(c(x1))
171.06/43.84	    c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	    c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	   TRS:
171.06/43.84	    a(x1) -> b(x1)
171.06/43.84	    b(b(a(x1))) -> c(x1)
171.06/43.84	    c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	   TDG Processor:
171.06/43.84	    DPs:
171.06/43.84	     a#(x1) -> b#(x1)
171.06/43.84	     b#(b(a(x1))) -> c#(x1)
171.06/43.84	     c#(a(x1)) -> c#(x1)
171.06/43.84	     c#(a(x1)) -> b#(c(x1))
171.06/43.84	     c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	     c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	    TRS:
171.06/43.84	     a(x1) -> b(x1)
171.06/43.84	     b(b(a(x1))) -> c(x1)
171.06/43.84	     c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	    graph:
171.06/43.84	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
171.06/43.84	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
171.06/43.84	     c#(a(x1)) -> b#(c(x1)) -> b#(b(a(x1))) -> c#(x1)
171.06/43.84	     c#(a(x1)) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
171.06/43.84	     c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
171.06/43.84	     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
171.06/43.84	     b#(b(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1)
171.06/43.84	     a#(x1) -> b#(x1) -> b#(b(a(x1))) -> c#(x1)
171.06/43.84	    Arctic Interpretation Processor:
171.06/43.84	     dimension: 2
171.06/43.84	     usable rules:
171.06/43.84	      a(x1) -> b(x1)
171.06/43.84	      b(b(a(x1))) -> c(x1)
171.06/43.84	      c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	     interpretation:
171.06/43.84	      [c#](x0) = [-& 0 ]x0 + [0],
171.06/43.84	      
171.06/43.84	      [b#](x0) = [0 0]x0,
171.06/43.84	      
171.06/43.84	      [a#](x0) = [0 0]x0 + [0],
171.06/43.84	      
171.06/43.84	                [-& 0 ]     [0]
171.06/43.84	      [c](x0) = [0  1 ]x0 + [0],
171.06/43.84	      
171.06/43.84	                [0  0 ]     [-&]
171.06/43.84	      [b](x0) = [0  -&]x0 + [0 ],
171.06/43.84	      
171.06/43.84	                [0 0]     [0]
171.06/43.84	      [a](x0) = [0 1]x0 + [1]
171.06/43.84	     orientation:
171.06/43.84	      a#(x1) = [0 0]x1 + [0] >= [0 0]x1 = b#(x1)
171.06/43.84	      
171.06/43.84	      b#(b(a(x1))) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = c#(x1)
171.06/43.84	      
171.06/43.84	      c#(a(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = c#(x1)
171.06/43.84	      
171.06/43.84	      c#(a(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [0] = b#(c(x1))
171.06/43.84	      
171.06/43.84	      c#(a(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [0] = a#(b(c(x1)))
171.06/43.84	      
171.06/43.84	      c#(a(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = a#(a(b(c(x1))))
171.06/43.84	      
171.06/43.84	              [0 0]     [0]    [0  0 ]     [-&]        
171.06/43.84	      a(x1) = [0 1]x1 + [1] >= [0  -&]x1 + [0 ] = b(x1)
171.06/43.84	      
171.06/43.84	                    [0 1]     [1]    [-& 0 ]     [0]        
171.06/43.84	      b(b(a(x1))) = [0 1]x1 + [1] >= [0  1 ]x1 + [0] = c(x1)
171.06/43.84	      
171.06/43.84	                 [0 1]     [1]    [0 1]     [1]                 
171.06/43.84	      c(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(a(b(c(x1))))
171.06/43.84	     problem:
171.06/43.84	      DPs:
171.06/43.84	       a#(x1) -> b#(x1)
171.06/43.84	       c#(a(x1)) -> b#(c(x1))
171.06/43.84	       c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	       c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	      TRS:
171.06/43.84	       a(x1) -> b(x1)
171.06/43.84	       b(b(a(x1))) -> c(x1)
171.06/43.84	       c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	     Restore Modifier:
171.06/43.84	      DPs:
171.06/43.84	       a#(x1) -> b#(x1)
171.06/43.84	       c#(a(x1)) -> b#(c(x1))
171.06/43.84	       c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	       c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	      TRS:
171.06/43.84	       a(x1) -> b(x1)
171.06/43.84	       b(b(a(x1))) -> c(x1)
171.06/43.84	       c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	      EDG Processor:
171.06/43.84	       DPs:
171.06/43.84	        a#(x1) -> b#(x1)
171.06/43.84	        c#(a(x1)) -> b#(c(x1))
171.06/43.84	        c#(a(x1)) -> a#(b(c(x1)))
171.06/43.84	        c#(a(x1)) -> a#(a(b(c(x1))))
171.06/43.84	       TRS:
171.06/43.84	        a(x1) -> b(x1)
171.06/43.84	        b(b(a(x1))) -> c(x1)
171.06/43.84	        c(a(x1)) -> a(a(b(c(x1))))
171.06/43.84	       graph:
171.06/43.84	        c#(a(x1)) -> a#(b(c(x1))) -> a#(x1) -> b#(x1)
171.06/43.84	        c#(a(x1)) -> a#(a(b(c(x1)))) -> a#(x1) -> b#(x1)
171.06/43.84	       SCC Processor:
171.06/43.84	        #sccs: 0
171.06/43.84	        #rules: 0
171.06/43.84	        #arcs: 2/16
171.06/43.84	        
171.06/43.85	EOF