183.83/47.01	YES
184.05/47.02	
184.05/47.02	Problem:
184.05/47.02	 a(x1) -> x1
184.05/47.02	 a(a(b(x1))) -> b(b(a(a(x1))))
184.05/47.02	 b(x1) -> a(c(a(x1)))
184.05/47.02	
184.05/47.02	Proof:
184.05/47.02	 String Reversal Processor:
184.05/47.02	  a(x1) -> x1
184.05/47.02	  b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	  b(x1) -> a(c(a(x1)))
184.05/47.02	  DP Processor:
184.05/47.02	   DPs:
184.05/47.02	    b#(a(a(x1))) -> b#(x1)
184.05/47.02	    b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	    b#(a(a(x1))) -> a#(b(b(x1)))
184.05/47.02	    b#(a(a(x1))) -> a#(a(b(b(x1))))
184.05/47.02	    b#(x1) -> a#(x1)
184.05/47.02	    b#(x1) -> a#(c(a(x1)))
184.05/47.02	   TRS:
184.05/47.02	    a(x1) -> x1
184.05/47.02	    b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	    b(x1) -> a(c(a(x1)))
184.05/47.02	   TDG Processor:
184.05/47.02	    DPs:
184.05/47.02	     b#(a(a(x1))) -> b#(x1)
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	     b#(a(a(x1))) -> a#(b(b(x1)))
184.05/47.02	     b#(a(a(x1))) -> a#(a(b(b(x1))))
184.05/47.02	     b#(x1) -> a#(x1)
184.05/47.02	     b#(x1) -> a#(c(a(x1)))
184.05/47.02	    TRS:
184.05/47.02	     a(x1) -> x1
184.05/47.02	     b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	     b(x1) -> a(c(a(x1)))
184.05/47.02	    graph:
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1)) -> b#(x1) -> a#(c(a(x1)))
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1)) -> b#(x1) -> a#(x1)
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(b(b(x1))))
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(b(b(x1)))
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1)
184.05/47.02	     b#(a(a(x1))) -> b#(x1) -> b#(x1) -> a#(c(a(x1)))
184.05/47.02	     b#(a(a(x1))) -> b#(x1) -> b#(x1) -> a#(x1)
184.05/47.02	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(b(x1))))
184.05/47.02	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(b(x1)))
184.05/47.02	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
184.05/47.02	    SCC Processor:
184.05/47.02	     #sccs: 1
184.05/47.02	     #rules: 2
184.05/47.02	     #arcs: 12/36
184.05/47.02	     DPs:
184.05/47.02	      b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	      b#(a(a(x1))) -> b#(x1)
184.05/47.02	     TRS:
184.05/47.02	      a(x1) -> x1
184.05/47.02	      b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	      b(x1) -> a(c(a(x1)))
184.05/47.02	     Arctic Interpretation Processor:
184.05/47.02	      dimension: 2
184.05/47.02	      usable rules:
184.05/47.02	       a(x1) -> x1
184.05/47.02	       b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	       b(x1) -> a(c(a(x1)))
184.05/47.02	      interpretation:
184.05/47.02	       [b#](x0) = [-& 0 ]x0 + [0],
184.05/47.02	       
184.05/47.02	                 [0 ]
184.05/47.02	       [c](x0) = [-&],
184.05/47.02	       
184.05/47.02	                 [0 0]     [0]
184.05/47.02	       [b](x0) = [0 0]x0 + [1],
184.05/47.02	       
184.05/47.02	                 [0 3]     [0]
184.05/47.02	       [a](x0) = [0 0]x0 + [1]
184.05/47.02	      orientation:
184.05/47.02	       b#(a(a(x1))) = [0 3]x1 + [1] >= [0 0]x1 + [1] = b#(b(x1))
184.05/47.02	       
184.05/47.02	       b#(a(a(x1))) = [0 3]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1)
184.05/47.02	       
184.05/47.02	               [0 3]     [0]           
184.05/47.02	       a(x1) = [0 0]x1 + [1] >= x1 = x1
184.05/47.02	       
184.05/47.02	                     [3 3]     [4]    [3 3]     [4]                 
184.05/47.02	       b(a(a(x1))) = [3 3]x1 + [4] >= [3 3]x1 + [4] = a(a(b(b(x1))))
184.05/47.02	       
184.05/47.02	               [0 0]     [0]    [0]              
184.05/47.02	       b(x1) = [0 0]x1 + [1] >= [1] = a(c(a(x1)))
184.05/47.02	      problem:
184.05/47.02	       DPs:
184.05/47.02	        b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	       TRS:
184.05/47.02	        a(x1) -> x1
184.05/47.02	        b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	        b(x1) -> a(c(a(x1)))
184.05/47.02	      Restore Modifier:
184.05/47.02	       DPs:
184.05/47.02	        b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	       TRS:
184.05/47.02	        a(x1) -> x1
184.05/47.02	        b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	        b(x1) -> a(c(a(x1)))
184.05/47.02	       EDG Processor:
184.05/47.02	        DPs:
184.05/47.02	         b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	        TRS:
184.05/47.02	         a(x1) -> x1
184.05/47.02	         b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	         b(x1) -> a(c(a(x1)))
184.05/47.02	        graph:
184.05/47.02	         b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
184.05/47.02	        Arctic Interpretation Processor:
184.05/47.02	         dimension: 2
184.05/47.02	         usable rules:
184.05/47.02	          a(x1) -> x1
184.05/47.02	          b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	          b(x1) -> a(c(a(x1)))
184.05/47.02	         interpretation:
184.05/47.02	          [b#](x0) = [1 0]x0 + [0],
184.05/47.02	          
184.05/47.02	                    [0]
184.05/47.02	          [c](x0) = [0],
184.05/47.02	          
184.05/47.02	                    [0  -&]     [0]
184.05/47.02	          [b](x0) = [2  0 ]x0 + [2],
184.05/47.02	          
184.05/47.02	                    [0 0]     [0]
184.05/47.02	          [a](x0) = [2 0]x0 + [2]
184.05/47.02	         orientation:
184.05/47.02	          b#(a(a(x1))) = [3 2]x1 + [3] >= [2 0]x1 + [2] = b#(b(x1))
184.05/47.02	          
184.05/47.02	                  [0 0]     [0]           
184.05/47.02	          a(x1) = [2 0]x1 + [2] >= x1 = x1
184.05/47.02	          
184.05/47.02	                        [2 0]     [2]    [2 0]     [2]                 
184.05/47.02	          b(a(a(x1))) = [4 2]x1 + [4] >= [4 2]x1 + [4] = a(a(b(b(x1))))
184.05/47.02	          
184.05/47.02	                  [0  -&]     [0]    [0]              
184.05/47.02	          b(x1) = [2  0 ]x1 + [2] >= [2] = a(c(a(x1)))
184.05/47.02	         problem:
184.05/47.02	          DPs:
184.05/47.02	           
184.05/47.02	          TRS:
184.05/47.02	           a(x1) -> x1
184.05/47.02	           b(a(a(x1))) -> a(a(b(b(x1))))
184.05/47.02	           b(x1) -> a(c(a(x1)))
184.05/47.02	         Qed
184.05/47.02	EOF