167.32/42.72	YES
167.32/42.72	
167.32/42.72	Problem:
167.32/42.72	 a(x1) -> x1
167.32/42.72	 a(b(x1)) -> a(c(b(b(c(x1)))))
167.32/42.72	 b(x1) -> x1
167.32/42.72	 c(c(x1)) -> a(x1)
167.32/42.72	
167.32/42.72	Proof:
167.32/42.72	 String Reversal Processor:
167.32/42.72	  a(x1) -> x1
167.32/42.72	  b(a(x1)) -> c(b(b(c(a(x1)))))
167.32/42.72	  b(x1) -> x1
167.32/42.72	  c(c(x1)) -> a(x1)
167.32/42.72	  DP Processor:
167.32/42.72	   DPs:
167.32/42.72	    b#(a(x1)) -> c#(a(x1))
167.32/42.72	    b#(a(x1)) -> b#(c(a(x1)))
167.32/42.72	    b#(a(x1)) -> b#(b(c(a(x1))))
167.32/42.72	    b#(a(x1)) -> c#(b(b(c(a(x1)))))
167.32/42.72	    c#(c(x1)) -> a#(x1)
167.32/42.72	   TRS:
167.32/42.72	    a(x1) -> x1
167.32/42.72	    b(a(x1)) -> c(b(b(c(a(x1)))))
167.32/42.72	    b(x1) -> x1
167.32/42.72	    c(c(x1)) -> a(x1)
167.32/42.72	   TDG Processor:
167.32/42.72	    DPs:
167.32/42.72	     b#(a(x1)) -> c#(a(x1))
167.32/42.72	     b#(a(x1)) -> b#(c(a(x1)))
167.32/42.72	     b#(a(x1)) -> b#(b(c(a(x1))))
167.32/42.72	     b#(a(x1)) -> c#(b(b(c(a(x1)))))
167.32/42.72	     c#(c(x1)) -> a#(x1)
167.32/42.72	    TRS:
167.32/42.72	     a(x1) -> x1
167.32/42.72	     b(a(x1)) -> c(b(b(c(a(x1)))))
167.32/42.72	     b(x1) -> x1
167.32/42.72	     c(c(x1)) -> a(x1)
167.32/42.72	    graph:
167.32/42.72	     b#(a(x1)) -> c#(b(b(c(a(x1))))) -> c#(c(x1)) -> a#(x1)
167.32/42.72	     b#(a(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
167.32/42.72	     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(b(b(c(a(x1)))))
167.32/42.72	     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(b(c(a(x1))))
167.32/42.72	     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(c(a(x1)))
167.32/42.72	     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(a(x1))
167.32/42.72	     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> c#(b(b(c(a(x1)))))
167.32/42.72	     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> b#(b(c(a(x1))))
167.32/42.72	     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> b#(c(a(x1)))
167.32/42.72	     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> c#(a(x1))
167.32/42.72	    SCC Processor:
167.32/42.72	     #sccs: 1
167.32/42.72	     #rules: 2
167.32/42.72	     #arcs: 10/25
167.32/42.72	     DPs:
167.32/42.72	      b#(a(x1)) -> b#(c(a(x1)))
167.32/42.72	      b#(a(x1)) -> b#(b(c(a(x1))))
167.32/42.72	     TRS:
167.32/42.72	      a(x1) -> x1
167.32/42.72	      b(a(x1)) -> c(b(b(c(a(x1)))))
167.32/42.72	      b(x1) -> x1
167.32/42.72	      c(c(x1)) -> a(x1)
167.32/42.72	     Arctic Interpretation Processor:
167.32/42.72	      dimension: 2
167.32/42.72	      usable rules:
167.32/42.72	       a(x1) -> x1
167.32/42.72	       b(a(x1)) -> c(b(b(c(a(x1)))))
167.32/42.72	       b(x1) -> x1
167.32/42.72	       c(c(x1)) -> a(x1)
167.32/42.72	      interpretation:
167.32/42.72	       [b#](x0) = [0  -&]x0 + [0],
167.32/42.72	       
167.32/42.72	                 [-& 0 ]     [0]
167.32/42.72	       [c](x0) = [0  2 ]x0 + [2],
167.32/42.72	       
167.32/42.72	                 [0  -&]     [0]
167.32/42.72	       [b](x0) = [2  0 ]x0 + [0],
167.32/42.72	       
167.32/42.72	                 [0  2 ]     [2]
167.32/42.72	       [a](x0) = [-& 0 ]x0 + [0]
167.32/42.72	      orientation:
167.32/42.72	       b#(a(x1)) = [0 2]x1 + [2] >= [-& 0 ]x1 + [0] = b#(c(a(x1)))
167.32/42.72	       
167.32/42.72	       b#(a(x1)) = [0 2]x1 + [2] >= [-& 0 ]x1 + [0] = b#(b(c(a(x1))))
167.32/42.72	       
167.32/42.72	               [0  2 ]     [2]           
167.32/42.72	       a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
167.32/42.72	       
167.32/42.72	                  [0 2]     [2]    [0 2]     [2]                    
167.32/42.72	       b(a(x1)) = [2 4]x1 + [4] >= [2 4]x1 + [4] = c(b(b(c(a(x1)))))
167.32/42.72	       
167.32/42.72	               [0  -&]     [0]           
167.32/42.72	       b(x1) = [2  0 ]x1 + [0] >= x1 = x1
167.32/42.72	       
167.32/42.72	                  [0 2]     [2]    [0  2 ]     [2]        
167.32/42.72	       c(c(x1)) = [2 4]x1 + [4] >= [-& 0 ]x1 + [0] = a(x1)
167.32/42.72	      problem:
167.32/42.72	       DPs:
167.32/42.72	        
167.32/42.72	       TRS:
167.32/42.72	        a(x1) -> x1
167.32/42.72	        b(a(x1)) -> c(b(b(c(a(x1)))))
167.32/42.72	        b(x1) -> x1
167.32/42.72	        c(c(x1)) -> a(x1)
167.32/42.72	      Qed
167.32/42.73	EOF