170.66/43.44	YES
170.66/43.45	
170.66/43.45	Problem:
170.66/43.45	 a(x1) -> x1
170.66/43.45	 a(b(x1)) -> x1
170.66/43.45	 a(c(x1)) -> c(c(a(a(b(x1)))))
170.66/43.45	 b(b(x1)) -> x1
170.66/43.45	
170.66/43.45	Proof:
170.66/43.45	 String Reversal Processor:
170.66/43.45	  a(x1) -> x1
170.66/43.45	  b(a(x1)) -> x1
170.66/43.45	  c(a(x1)) -> b(a(a(c(c(x1)))))
170.66/43.45	  b(b(x1)) -> x1
170.66/43.45	  DP Processor:
170.66/43.45	   DPs:
170.66/43.45	    c#(a(x1)) -> c#(x1)
170.66/43.45	    c#(a(x1)) -> c#(c(x1))
170.66/43.45	    c#(a(x1)) -> a#(c(c(x1)))
170.66/43.45	    c#(a(x1)) -> a#(a(c(c(x1))))
170.66/43.45	    c#(a(x1)) -> b#(a(a(c(c(x1)))))
170.66/43.45	   TRS:
170.66/43.45	    a(x1) -> x1
170.66/43.45	    b(a(x1)) -> x1
170.66/43.45	    c(a(x1)) -> b(a(a(c(c(x1)))))
170.66/43.45	    b(b(x1)) -> x1
170.66/43.45	   TDG Processor:
170.66/43.45	    DPs:
170.66/43.45	     c#(a(x1)) -> c#(x1)
170.66/43.45	     c#(a(x1)) -> c#(c(x1))
170.66/43.45	     c#(a(x1)) -> a#(c(c(x1)))
170.66/43.45	     c#(a(x1)) -> a#(a(c(c(x1))))
170.66/43.45	     c#(a(x1)) -> b#(a(a(c(c(x1)))))
170.66/43.45	    TRS:
170.66/43.45	     a(x1) -> x1
170.66/43.45	     b(a(x1)) -> x1
170.66/43.45	     c(a(x1)) -> b(a(a(c(c(x1)))))
170.66/43.45	     b(b(x1)) -> x1
170.66/43.45	    graph:
170.66/43.45	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(a(a(c(c(x1)))))
170.66/43.45	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(a(c(c(x1))))
170.66/43.45	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(c(c(x1)))
170.66/43.45	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
170.66/43.45	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1)
170.66/43.45	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(a(c(c(x1)))))
170.66/43.45	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(c(c(x1))))
170.66/43.45	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(c(x1)))
170.66/43.45	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1))
170.66/43.45	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
170.66/43.45	    SCC Processor:
170.66/43.45	     #sccs: 1
170.66/43.45	     #rules: 2
170.66/43.45	     #arcs: 10/25
170.66/43.45	     DPs:
170.66/43.45	      c#(a(x1)) -> c#(c(x1))
170.66/43.45	      c#(a(x1)) -> c#(x1)
170.66/43.45	     TRS:
170.66/43.45	      a(x1) -> x1
170.66/43.45	      b(a(x1)) -> x1
170.66/43.45	      c(a(x1)) -> b(a(a(c(c(x1)))))
170.66/43.45	      b(b(x1)) -> x1
170.66/43.45	     Arctic Interpretation Processor:
170.66/43.45	      dimension: 2
170.66/43.45	      usable rules:
170.66/43.45	       a(x1) -> x1
170.66/43.45	       b(a(x1)) -> x1
170.66/43.45	       c(a(x1)) -> b(a(a(c(c(x1)))))
170.66/43.45	       b(b(x1)) -> x1
170.66/43.45	      interpretation:
170.66/43.45	       [c#](x0) = [1 0]x0 + [2],
170.66/43.45	       
170.66/43.45	                 [0  -&]     [-&]
170.66/43.45	       [c](x0) = [1  0 ]x0 + [1 ],
170.66/43.45	       
170.66/43.45	                 [-& 0 ]     [0]
170.66/43.45	       [b](x0) = [0  1 ]x0 + [1],
170.66/43.45	       
170.66/43.45	                 [1 0]     [2]
170.66/43.45	       [a](x0) = [0 0]x0 + [0]
170.66/43.45	      orientation:
170.66/43.45	       c#(a(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = c#(c(x1))
170.66/43.45	       
170.66/43.45	       c#(a(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = c#(x1)
170.66/43.45	       
170.66/43.45	               [1 0]     [2]           
170.66/43.45	       a(x1) = [0 0]x1 + [0] >= x1 = x1
170.66/43.45	       
170.66/43.45	                  [0 0]     [0]           
170.66/43.45	       b(a(x1)) = [1 1]x1 + [2] >= x1 = x1
170.66/43.45	       
170.66/43.45	                  [1 0]     [2]    [1 0]     [2]                    
170.66/43.45	       c(a(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = b(a(a(c(c(x1)))))
170.66/43.45	       
170.66/43.45	                  [0 1]     [1]           
170.66/43.45	       b(b(x1)) = [1 2]x1 + [2] >= x1 = x1
170.66/43.45	      problem:
170.66/43.45	       DPs:
170.66/43.45	        
170.66/43.45	       TRS:
170.66/43.45	        a(x1) -> x1
170.66/43.45	        b(a(x1)) -> x1
170.66/43.45	        c(a(x1)) -> b(a(a(c(c(x1)))))
170.66/43.45	        b(b(x1)) -> x1
170.66/43.45	      Qed
170.66/43.45	EOF