168.99/43.03	YES
168.99/43.03	
168.99/43.03	Problem:
168.99/43.03	 a(a(b(x1))) -> c(x1)
168.99/43.03	 a(c(x1)) -> b(c(a(a(x1))))
168.99/43.03	 b(c(x1)) -> x1
168.99/43.03	
168.99/43.03	Proof:
168.99/43.03	 String Reversal Processor:
168.99/43.03	  b(a(a(x1))) -> c(x1)
168.99/43.03	  c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	  c(b(x1)) -> x1
168.99/43.03	  DP Processor:
168.99/43.03	   DPs:
168.99/43.03	    b#(a(a(x1))) -> c#(x1)
168.99/43.03	    c#(a(x1)) -> b#(x1)
168.99/43.03	    c#(a(x1)) -> c#(b(x1))
168.99/43.03	   TRS:
168.99/43.03	    b(a(a(x1))) -> c(x1)
168.99/43.03	    c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	    c(b(x1)) -> x1
168.99/43.03	   TDG Processor:
168.99/43.03	    DPs:
168.99/43.03	     b#(a(a(x1))) -> c#(x1)
168.99/43.03	     c#(a(x1)) -> b#(x1)
168.99/43.03	     c#(a(x1)) -> c#(b(x1))
168.99/43.03	    TRS:
168.99/43.03	     b(a(a(x1))) -> c(x1)
168.99/43.03	     c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	     c(b(x1)) -> x1
168.99/43.03	    graph:
168.99/43.03	     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(b(x1))
168.99/43.03	     c#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(x1)
168.99/43.03	     c#(a(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
168.99/43.03	     b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(b(x1))
168.99/43.03	     b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(x1)
168.99/43.03	    Arctic Interpretation Processor:
168.99/43.03	     dimension: 1
168.99/43.03	     usable rules:
168.99/43.03	      b(a(a(x1))) -> c(x1)
168.99/43.03	      c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	      c(b(x1)) -> x1
168.99/43.03	     interpretation:
168.99/43.03	      [c#](x0) = 2x0 + 3,
168.99/43.03	      
168.99/43.03	      [b#](x0) = x0 + 6,
168.99/43.03	      
168.99/43.03	      [c](x0) = 1x0 + 0,
168.99/43.03	      
168.99/43.03	      [a](x0) = 1x0 + 4,
168.99/43.03	      
168.99/43.03	      [b](x0) = -1x0 + 0
168.99/43.03	     orientation:
168.99/43.03	      b#(a(a(x1))) = 2x1 + 6 >= 2x1 + 3 = c#(x1)
168.99/43.03	      
168.99/43.03	      c#(a(x1)) = 3x1 + 6 >= x1 + 6 = b#(x1)
168.99/43.03	      
168.99/43.03	      c#(a(x1)) = 3x1 + 6 >= 1x1 + 3 = c#(b(x1))
168.99/43.03	      
168.99/43.03	      b(a(a(x1))) = 1x1 + 4 >= 1x1 + 0 = c(x1)
168.99/43.03	      
168.99/43.03	      c(a(x1)) = 2x1 + 5 >= 2x1 + 5 = a(a(c(b(x1))))
168.99/43.03	      
168.99/43.03	      c(b(x1)) = x1 + 1 >= x1 = x1
168.99/43.03	     problem:
168.99/43.03	      DPs:
168.99/43.03	       b#(a(a(x1))) -> c#(x1)
168.99/43.03	       c#(a(x1)) -> b#(x1)
168.99/43.03	      TRS:
168.99/43.03	       b(a(a(x1))) -> c(x1)
168.99/43.03	       c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	       c(b(x1)) -> x1
168.99/43.03	     Restore Modifier:
168.99/43.03	      DPs:
168.99/43.03	       b#(a(a(x1))) -> c#(x1)
168.99/43.03	       c#(a(x1)) -> b#(x1)
168.99/43.03	      TRS:
168.99/43.03	       b(a(a(x1))) -> c(x1)
168.99/43.03	       c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	       c(b(x1)) -> x1
168.99/43.03	      EDG Processor:
168.99/43.03	       DPs:
168.99/43.03	        b#(a(a(x1))) -> c#(x1)
168.99/43.03	        c#(a(x1)) -> b#(x1)
168.99/43.03	       TRS:
168.99/43.03	        b(a(a(x1))) -> c(x1)
168.99/43.03	        c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	        c(b(x1)) -> x1
168.99/43.03	       graph:
168.99/43.03	        c#(a(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
168.99/43.03	        b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(x1)
168.99/43.03	       Usable Rule Processor:
168.99/43.03	        DPs:
168.99/43.03	         b#(a(a(x1))) -> c#(x1)
168.99/43.03	         c#(a(x1)) -> b#(x1)
168.99/43.03	        TRS:
168.99/43.03	         
168.99/43.03	        Arctic Interpretation Processor:
168.99/43.03	         dimension: 1
168.99/43.03	         usable rules:
168.99/43.03	          
168.99/43.03	         interpretation:
168.99/43.03	          [c#](x0) = 8x0 + 2,
168.99/43.03	          
168.99/43.03	          [b#](x0) = 12x0 + 0,
168.99/43.03	          
168.99/43.03	          [a](x0) = 4x0 + 7
168.99/43.03	         orientation:
168.99/43.03	          b#(a(a(x1))) = 20x1 + 23 >= 8x1 + 2 = c#(x1)
168.99/43.03	          
168.99/43.03	          c#(a(x1)) = 12x1 + 15 >= 12x1 + 0 = b#(x1)
168.99/43.03	         problem:
168.99/43.03	          DPs:
168.99/43.03	           c#(a(x1)) -> b#(x1)
168.99/43.03	          TRS:
168.99/43.03	           
168.99/43.03	         Restore Modifier:
168.99/43.03	          DPs:
168.99/43.03	           c#(a(x1)) -> b#(x1)
168.99/43.03	          TRS:
168.99/43.03	           b(a(a(x1))) -> c(x1)
168.99/43.03	           c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	           c(b(x1)) -> x1
168.99/43.03	          EDG Processor:
168.99/43.03	           DPs:
168.99/43.03	            c#(a(x1)) -> b#(x1)
168.99/43.03	           TRS:
168.99/43.03	            b(a(a(x1))) -> c(x1)
168.99/43.03	            c(a(x1)) -> a(a(c(b(x1))))
168.99/43.03	            c(b(x1)) -> x1
168.99/43.03	           graph:
168.99/43.03	            
168.99/43.03	           SCC Processor:
168.99/43.03	            #sccs: 0
168.99/43.03	            #rules: 0
168.99/43.03	            #arcs: 0/1
168.99/43.03	            
168.99/43.04	EOF