189.35/47.66	YES
189.35/47.67	
189.35/47.67	Problem:
189.35/47.67	 a(x1) -> x1
189.35/47.67	 a(b(x1)) -> b(b(a(a(c(a(x1))))))
189.35/47.67	 c(c(a(x1))) -> x1
189.35/47.67	
189.35/47.67	Proof:
189.35/47.67	 String Reversal Processor:
189.35/47.67	  a(x1) -> x1
189.35/47.67	  b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	  a(c(c(x1))) -> x1
189.35/47.67	  DP Processor:
189.35/47.67	   DPs:
189.35/47.67	    b#(a(x1)) -> b#(x1)
189.35/47.67	    b#(a(x1)) -> b#(b(x1))
189.35/47.67	    b#(a(x1)) -> a#(b(b(x1)))
189.35/47.67	    b#(a(x1)) -> a#(a(b(b(x1))))
189.35/47.67	    b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
189.35/47.67	   TRS:
189.35/47.67	    a(x1) -> x1
189.35/47.67	    b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	    a(c(c(x1))) -> x1
189.35/47.67	   TDG Processor:
189.35/47.67	    DPs:
189.35/47.67	     b#(a(x1)) -> b#(x1)
189.35/47.67	     b#(a(x1)) -> b#(b(x1))
189.35/47.67	     b#(a(x1)) -> a#(b(b(x1)))
189.35/47.67	     b#(a(x1)) -> a#(a(b(b(x1))))
189.35/47.67	     b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
189.35/47.67	    TRS:
189.35/47.67	     a(x1) -> x1
189.35/47.67	     b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	     a(c(c(x1))) -> x1
189.35/47.67	    graph:
189.35/47.67	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
189.35/47.67	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(a(b(b(x1))))
189.35/47.67	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
189.35/47.67	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
189.35/47.67	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
189.35/47.67	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(a(a(b(b(x1))))))
189.35/47.67	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(b(x1))))
189.35/47.67	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
189.35/47.67	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
189.35/47.67	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
189.35/47.67	    SCC Processor:
189.35/47.67	     #sccs: 1
189.35/47.67	     #rules: 2
189.35/47.67	     #arcs: 10/25
189.35/47.67	     DPs:
189.35/47.67	      b#(a(x1)) -> b#(b(x1))
189.35/47.67	      b#(a(x1)) -> b#(x1)
189.35/47.67	     TRS:
189.35/47.67	      a(x1) -> x1
189.35/47.67	      b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	      a(c(c(x1))) -> x1
189.35/47.67	     Arctic Interpretation Processor:
189.35/47.67	      dimension: 3
189.35/47.67	      usable rules:
189.35/47.67	       a(x1) -> x1
189.35/47.67	       b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	       a(c(c(x1))) -> x1
189.35/47.67	      interpretation:
189.35/47.67	       [b#](x0) = [0  -& 1 ]x0 + [0],
189.35/47.67	       
189.35/47.67	                 [-& -& -&]     [0]
189.35/47.67	       [c](x0) = [0  0  0 ]x0 + [0]
189.35/47.67	                 [-& 0  -&]     [0],
189.35/47.67	       
189.35/47.67	                 [-& -& 0 ]     [0]
189.35/47.67	       [b](x0) = [0  -& 1 ]x0 + [0]
189.35/47.67	                 [0  -& -&]     [0],
189.35/47.67	       
189.35/47.67	                 [1  -& 0 ]     [1]
189.35/47.67	       [a](x0) = [0  0  0 ]x0 + [1]
189.35/47.67	                 [1  -& 0 ]     [1]
189.35/47.67	      orientation:
189.35/47.67	       b#(a(x1)) = [2  -& 1 ]x1 + [2] >= [1  -& 0 ]x1 + [1] = b#(b(x1))
189.35/47.67	       
189.35/47.67	       b#(a(x1)) = [2  -& 1 ]x1 + [2] >= [0  -& 1 ]x1 + [0] = b#(x1)
189.35/47.67	       
189.35/47.67	               [1  -& 0 ]     [1]           
189.35/47.67	       a(x1) = [0  0  0 ]x1 + [1] >= x1 = x1
189.35/47.67	               [1  -& 0 ]     [1]           
189.35/47.67	       
189.35/47.67	                  [1  -& 0 ]     [1]    [1  -& 0 ]     [1]                       
189.35/47.67	       b(a(x1)) = [2  -& 1 ]x1 + [2] >= [2  -& 1 ]x1 + [2] = a(c(a(a(b(b(x1))))))
189.35/47.67	                  [1  -& 0 ]     [1]    [1  -& 0 ]     [1]                       
189.35/47.67	       
189.35/47.67	                     [0 0 0]     [1]           
189.35/47.67	       a(c(c(x1))) = [0 0 0]x1 + [1] >= x1 = x1
189.35/47.67	                     [0 0 0]     [1]           
189.35/47.67	      problem:
189.35/47.67	       DPs:
189.35/47.67	        b#(a(x1)) -> b#(x1)
189.35/47.67	       TRS:
189.35/47.67	        a(x1) -> x1
189.35/47.67	        b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	        a(c(c(x1))) -> x1
189.35/47.67	      Restore Modifier:
189.35/47.67	       DPs:
189.35/47.67	        b#(a(x1)) -> b#(x1)
189.35/47.67	       TRS:
189.35/47.67	        a(x1) -> x1
189.35/47.67	        b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	        a(c(c(x1))) -> x1
189.35/47.67	       EDG Processor:
189.35/47.67	        DPs:
189.35/47.67	         b#(a(x1)) -> b#(x1)
189.35/47.67	        TRS:
189.35/47.67	         a(x1) -> x1
189.35/47.67	         b(a(x1)) -> a(c(a(a(b(b(x1))))))
189.35/47.67	         a(c(c(x1))) -> x1
189.35/47.67	        graph:
189.35/47.67	         b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
189.35/47.67	        Usable Rule Processor:
189.35/47.67	         DPs:
189.35/47.67	          b#(a(x1)) -> b#(x1)
189.35/47.67	         TRS:
189.35/47.67	          
189.35/47.67	         Arctic Interpretation Processor:
189.35/47.67	          dimension: 4
189.35/47.67	          usable rules:
189.35/47.67	           
189.35/47.67	          interpretation:
189.35/47.67	           [b#](x0) = [0  -& -& -&]x0,
189.35/47.67	           
189.35/47.67	                     [1 0 0 0]     [0]
189.35/47.67	                     [0 0 0 0]     [0]
189.35/47.67	           [a](x0) = [1 0 0 0]x0 + [0]
189.35/47.67	                     [0 0 0 0]     [0]
189.35/47.67	          orientation:
189.35/47.67	           b#(a(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = b#(x1)
189.35/47.67	          problem:
189.35/47.67	           DPs:
189.35/47.67	            
189.35/47.67	           TRS:
189.35/47.67	            
189.35/47.67	          Qed
189.35/47.67	EOF