169.38/43.36	YES
169.38/43.36	
169.38/43.36	Problem:
169.38/43.36	 a(x1) -> x1
169.38/43.36	 a(a(b(x1))) -> b(b(a(a(x1))))
169.38/43.36	 b(x1) -> c(a(x1))
169.38/43.36	
169.38/43.36	Proof:
169.38/43.36	 String Reversal Processor:
169.38/43.36	  a(x1) -> x1
169.38/43.36	  b(a(a(x1))) -> a(a(b(b(x1))))
169.38/43.36	  b(x1) -> a(c(x1))
169.38/43.36	  DP Processor:
169.38/43.36	   DPs:
169.38/43.36	    b#(a(a(x1))) -> b#(x1)
169.38/43.36	    b#(a(a(x1))) -> b#(b(x1))
169.38/43.36	    b#(a(a(x1))) -> a#(b(b(x1)))
169.38/43.36	    b#(a(a(x1))) -> a#(a(b(b(x1))))
169.38/43.36	    b#(x1) -> a#(c(x1))
169.38/43.36	   TRS:
169.38/43.36	    a(x1) -> x1
169.38/43.36	    b(a(a(x1))) -> a(a(b(b(x1))))
169.38/43.36	    b(x1) -> a(c(x1))
169.38/43.36	   TDG Processor:
169.38/43.36	    DPs:
169.38/43.36	     b#(a(a(x1))) -> b#(x1)
169.38/43.36	     b#(a(a(x1))) -> b#(b(x1))
169.38/43.36	     b#(a(a(x1))) -> a#(b(b(x1)))
169.38/43.36	     b#(a(a(x1))) -> a#(a(b(b(x1))))
169.38/43.36	     b#(x1) -> a#(c(x1))
169.38/43.36	    TRS:
169.38/43.36	     a(x1) -> x1
169.38/43.36	     b(a(a(x1))) -> a(a(b(b(x1))))
169.38/43.36	     b(x1) -> a(c(x1))
169.38/43.36	    graph:
169.38/43.36	     b#(a(a(x1))) -> b#(b(x1)) -> b#(x1) -> a#(c(x1))
169.38/43.36	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(b(b(x1))))
169.38/43.36	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(b(b(x1)))
169.38/43.36	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
169.38/43.36	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1)
169.38/43.36	     b#(a(a(x1))) -> b#(x1) -> b#(x1) -> a#(c(x1))
169.38/43.36	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(b(x1))))
169.38/43.36	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(b(x1)))
169.38/43.36	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1))
169.38/43.36	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
169.38/43.36	    SCC Processor:
169.38/43.36	     #sccs: 1
169.38/43.36	     #rules: 2
169.38/43.36	     #arcs: 10/25
169.38/43.36	     DPs:
169.38/43.36	      b#(a(a(x1))) -> b#(b(x1))
169.38/43.36	      b#(a(a(x1))) -> b#(x1)
169.38/43.36	     TRS:
169.38/43.36	      a(x1) -> x1
169.38/43.36	      b(a(a(x1))) -> a(a(b(b(x1))))
169.38/43.36	      b(x1) -> a(c(x1))
169.38/43.36	     Arctic Interpretation Processor:
169.38/43.36	      dimension: 2
169.38/43.36	      usable rules:
169.38/43.36	       a(x1) -> x1
169.38/43.36	       b(a(a(x1))) -> a(a(b(b(x1))))
169.38/43.36	       b(x1) -> a(c(x1))
169.38/43.36	      interpretation:
169.38/43.36	       [b#](x0) = [0 0]x0 + [0],
169.38/43.36	       
169.38/43.36	                 [0  -&]     [0 ]
169.38/43.36	       [c](x0) = [-& -&]x0 + [-&],
169.38/43.36	       
169.38/43.36	                 [0 0]     [0]
169.38/43.36	       [b](x0) = [0 0]x0 + [0],
169.38/43.36	       
169.38/43.36	                 [0 1]     [0]
169.38/43.36	       [a](x0) = [0 0]x0 + [0]
169.38/43.36	      orientation:
169.38/43.36	       b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(b(x1))
169.38/43.36	       
169.38/43.36	       b#(a(a(x1))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(x1)
169.38/43.36	       
169.38/43.36	               [0 1]     [0]           
169.38/43.36	       a(x1) = [0 0]x1 + [0] >= x1 = x1
169.38/43.36	       
169.38/43.36	                     [1 1]     [1]    [1 1]     [1]                 
169.38/43.36	       b(a(a(x1))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(a(b(b(x1))))
169.38/43.36	       
169.38/43.36	               [0 0]     [0]    [0  -&]     [0]           
169.38/43.36	       b(x1) = [0 0]x1 + [0] >= [0  -&]x1 + [0] = a(c(x1))
169.38/43.36	      problem:
169.38/43.36	       DPs:
169.38/43.36	        
169.38/43.36	       TRS:
169.38/43.36	        a(x1) -> x1
169.38/43.36	        b(a(a(x1))) -> a(a(b(b(x1))))
169.38/43.36	        b(x1) -> a(c(x1))
169.38/43.36	      Qed
169.38/43.37	EOF