169.45/43.30	YES
169.45/43.30	
169.45/43.30	Problem:
169.45/43.30	 a(x1) -> x1
169.45/43.30	 a(b(x1)) -> b(b(a(a(c(x1)))))
169.45/43.30	 b(x1) -> x1
169.45/43.30	 c(b(c(x1))) -> x1
169.45/43.30	
169.45/43.30	Proof:
169.45/43.30	 String Reversal Processor:
169.45/43.30	  a(x1) -> x1
169.45/43.30	  b(a(x1)) -> c(a(a(b(b(x1)))))
169.45/43.30	  b(x1) -> x1
169.45/43.30	  c(b(c(x1))) -> x1
169.45/43.30	  DP Processor:
169.45/43.30	   DPs:
169.45/43.30	    b#(a(x1)) -> b#(x1)
169.45/43.30	    b#(a(x1)) -> b#(b(x1))
169.45/43.30	    b#(a(x1)) -> a#(b(b(x1)))
169.45/43.30	    b#(a(x1)) -> a#(a(b(b(x1))))
169.45/43.30	    b#(a(x1)) -> c#(a(a(b(b(x1)))))
169.45/43.30	   TRS:
169.45/43.30	    a(x1) -> x1
169.45/43.30	    b(a(x1)) -> c(a(a(b(b(x1)))))
169.45/43.30	    b(x1) -> x1
169.45/43.30	    c(b(c(x1))) -> x1
169.45/43.30	   TDG Processor:
169.45/43.30	    DPs:
169.45/43.30	     b#(a(x1)) -> b#(x1)
169.45/43.30	     b#(a(x1)) -> b#(b(x1))
169.45/43.30	     b#(a(x1)) -> a#(b(b(x1)))
169.45/43.30	     b#(a(x1)) -> a#(a(b(b(x1))))
169.45/43.30	     b#(a(x1)) -> c#(a(a(b(b(x1)))))
169.45/43.30	    TRS:
169.45/43.30	     a(x1) -> x1
169.45/43.30	     b(a(x1)) -> c(a(a(b(b(x1)))))
169.45/43.30	     b(x1) -> x1
169.45/43.30	     c(b(c(x1))) -> x1
169.45/43.30	    graph:
169.45/43.30	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
169.45/43.30	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(a(b(b(x1))))
169.45/43.30	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
169.45/43.30	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
169.45/43.30	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
169.45/43.30	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(a(b(b(x1)))))
169.45/43.30	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(b(x1))))
169.45/43.30	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
169.45/43.30	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
169.45/43.30	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
169.45/43.30	    SCC Processor:
169.45/43.30	     #sccs: 1
169.45/43.30	     #rules: 2
169.45/43.30	     #arcs: 10/25
169.45/43.30	     DPs:
169.45/43.30	      b#(a(x1)) -> b#(b(x1))
169.45/43.30	      b#(a(x1)) -> b#(x1)
169.45/43.30	     TRS:
169.45/43.30	      a(x1) -> x1
169.45/43.30	      b(a(x1)) -> c(a(a(b(b(x1)))))
169.45/43.30	      b(x1) -> x1
169.45/43.30	      c(b(c(x1))) -> x1
169.45/43.30	     Arctic Interpretation Processor:
169.45/43.30	      dimension: 2
169.45/43.30	      usable rules:
169.45/43.30	       a(x1) -> x1
169.45/43.30	       b(a(x1)) -> c(a(a(b(b(x1)))))
169.45/43.30	       b(x1) -> x1
169.45/43.30	       c(b(c(x1))) -> x1
169.45/43.30	      interpretation:
169.45/43.30	       [b#](x0) = [0 2]x0 + [2],
169.45/43.30	       
169.45/43.30	                 [0  0 ]     [0]
169.45/43.30	       [c](x0) = [0  -&]x0 + [0],
169.45/43.30	       
169.45/43.30	                 [0  1 ]  
169.45/43.30	       [b](x0) = [-& 0 ]x0,
169.45/43.30	       
169.45/43.30	                 [0 0]     [-&]
169.45/43.30	       [a](x0) = [0 1]x0 + [2 ]
169.45/43.30	      orientation:
169.45/43.30	       b#(a(x1)) = [2 3]x1 + [4] >= [0 2]x1 + [2] = b#(b(x1))
169.45/43.30	       
169.45/43.30	       b#(a(x1)) = [2 3]x1 + [4] >= [0 2]x1 + [2] = b#(x1)
169.45/43.30	       
169.45/43.30	               [0 0]     [-&]           
169.45/43.30	       a(x1) = [0 1]x1 + [2 ] >= x1 = x1
169.45/43.30	       
169.45/43.30	                  [1 2]     [3]    [1 2]     [3]                    
169.45/43.30	       b(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = c(a(a(b(b(x1)))))
169.45/43.30	       
169.45/43.30	               [0  1 ]             
169.45/43.30	       b(x1) = [-& 0 ]x1 >= x1 = x1
169.45/43.30	       
169.45/43.30	                     [1 0]     [1]           
169.45/43.30	       c(b(c(x1))) = [1 0]x1 + [1] >= x1 = x1
169.45/43.30	      problem:
169.45/43.30	       DPs:
169.45/43.30	        
169.45/43.30	       TRS:
169.45/43.30	        a(x1) -> x1
169.45/43.30	        b(a(x1)) -> c(a(a(b(b(x1)))))
169.45/43.30	        b(x1) -> x1
169.45/43.30	        c(b(c(x1))) -> x1
169.45/43.30	      Qed
169.45/43.31	EOF