174.13/44.50	YES
174.21/44.51	
174.21/44.51	Problem:
174.21/44.51	 a(x1) -> x1
174.21/44.51	 a(a(b(x1))) -> b(b(c(a(a(a(x1))))))
174.21/44.51	 c(a(x1)) -> x1
174.21/44.51	
174.21/44.51	Proof:
174.21/44.51	 String Reversal Processor:
174.21/44.51	  a(x1) -> x1
174.21/44.51	  b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
174.21/44.51	  a(c(x1)) -> x1
174.21/44.51	  DP Processor:
174.21/44.51	   DPs:
174.21/44.51	    b#(a(a(x1))) -> b#(x1)
174.21/44.51	    b#(a(a(x1))) -> b#(b(x1))
174.21/44.51	    b#(a(a(x1))) -> a#(c(b(b(x1))))
174.21/44.51	    b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
174.21/44.51	    b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
174.21/44.51	   TRS:
174.21/44.51	    a(x1) -> x1
174.21/44.51	    b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
174.21/44.51	    a(c(x1)) -> x1
174.21/44.51	   TDG Processor:
174.21/44.51	    DPs:
174.21/44.51	     b#(a(a(x1))) -> b#(x1)
174.21/44.51	     b#(a(a(x1))) -> b#(b(x1))
174.21/44.51	     b#(a(a(x1))) -> a#(c(b(b(x1))))
174.21/44.51	     b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
174.21/44.51	     b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
174.21/44.51	    TRS:
174.21/44.51	     a(x1) -> x1
174.21/44.51	     b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
174.21/44.51	     a(c(x1)) -> x1
174.21/44.51	    graph:
174.21/44.51	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
174.21/44.51	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
174.21/44.51	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(c(b(b(x1))))
174.21/44.51	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1))
174.21/44.51	     b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1)
174.21/44.51	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(a(c(b(b(x1))))))
174.21/44.51	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(c(b(b(x1)))))
174.21/44.51	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(c(b(b(x1))))
174.21/44.51	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1))
174.21/44.51	     b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1)
174.21/44.51	    SCC Processor:
174.21/44.51	     #sccs: 1
174.21/44.51	     #rules: 2
174.21/44.51	     #arcs: 10/25
174.21/44.51	     DPs:
174.21/44.51	      b#(a(a(x1))) -> b#(b(x1))
174.21/44.51	      b#(a(a(x1))) -> b#(x1)
174.21/44.51	     TRS:
174.21/44.51	      a(x1) -> x1
174.21/44.51	      b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
174.21/44.51	      a(c(x1)) -> x1
174.21/44.51	     Arctic Interpretation Processor:
174.21/44.51	      dimension: 2
174.21/44.51	      usable rules:
174.21/44.51	       a(x1) -> x1
174.21/44.51	       b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
174.21/44.51	       a(c(x1)) -> x1
174.21/44.51	      interpretation:
174.21/44.51	       [b#](x0) = [0 1]x0 + [3],
174.21/44.51	       
174.21/44.51	                 [-& -&]     [0]
174.21/44.51	       [c](x0) = [0  0 ]x0 + [3],
174.21/44.51	       
174.21/44.51	                 [0 0]     [0]
174.21/44.51	       [b](x0) = [0 0]x0 + [0],
174.21/44.51	       
174.21/44.51	                 [0 0]     [3]
174.21/44.51	       [a](x0) = [1 0]x0 + [0]
174.21/44.51	      orientation:
174.21/44.51	       b#(a(a(x1))) = [2 2]x1 + [5] >= [1 1]x1 + [3] = b#(b(x1))
174.21/44.51	       
174.21/44.51	       b#(a(a(x1))) = [2 2]x1 + [5] >= [0 1]x1 + [3] = b#(x1)
174.21/44.51	       
174.21/44.51	               [0 0]     [3]           
174.21/44.51	       a(x1) = [1 0]x1 + [0] >= x1 = x1
174.21/44.51	       
174.21/44.51	                     [1 1]     [4]    [1 1]     [4]                       
174.21/44.51	       b(a(a(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = a(a(a(c(b(b(x1))))))
174.21/44.51	       
174.21/44.51	                  [0 0]     [3]           
174.21/44.51	       a(c(x1)) = [0 0]x1 + [3] >= x1 = x1
174.21/44.51	      problem:
174.21/44.51	       DPs:
174.21/44.51	        
174.21/44.51	       TRS:
174.21/44.51	        a(x1) -> x1
174.21/44.51	        b(a(a(x1))) -> a(a(a(c(b(b(x1))))))
174.21/44.51	        a(c(x1)) -> x1
174.21/44.51	      Qed
174.21/44.51	EOF