167.13/42.61	YES
167.13/42.62	
167.13/42.62	Problem:
167.13/42.62	 a(x1) -> x1
167.13/42.62	 a(b(x1)) -> b(b(a(c(x1))))
167.13/42.62	 b(x1) -> x1
167.13/42.62	 c(b(c(x1))) -> a(x1)
167.13/42.62	
167.13/42.62	Proof:
167.13/42.62	 String Reversal Processor:
167.13/42.62	  a(x1) -> x1
167.13/42.62	  b(a(x1)) -> c(a(b(b(x1))))
167.13/42.62	  b(x1) -> x1
167.13/42.62	  c(b(c(x1))) -> a(x1)
167.13/42.62	  DP Processor:
167.13/42.62	   DPs:
167.13/42.62	    b#(a(x1)) -> b#(x1)
167.13/42.62	    b#(a(x1)) -> b#(b(x1))
167.13/42.62	    b#(a(x1)) -> a#(b(b(x1)))
167.13/42.62	    b#(a(x1)) -> c#(a(b(b(x1))))
167.13/42.62	    c#(b(c(x1))) -> a#(x1)
167.13/42.62	   TRS:
167.13/42.62	    a(x1) -> x1
167.13/42.62	    b(a(x1)) -> c(a(b(b(x1))))
167.13/42.62	    b(x1) -> x1
167.13/42.62	    c(b(c(x1))) -> a(x1)
167.13/42.62	   TDG Processor:
167.13/42.62	    DPs:
167.13/42.62	     b#(a(x1)) -> b#(x1)
167.13/42.62	     b#(a(x1)) -> b#(b(x1))
167.13/42.62	     b#(a(x1)) -> a#(b(b(x1)))
167.13/42.62	     b#(a(x1)) -> c#(a(b(b(x1))))
167.13/42.62	     c#(b(c(x1))) -> a#(x1)
167.13/42.62	    TRS:
167.13/42.62	     a(x1) -> x1
167.13/42.62	     b(a(x1)) -> c(a(b(b(x1))))
167.13/42.62	     b(x1) -> x1
167.13/42.62	     c(b(c(x1))) -> a(x1)
167.13/42.62	    graph:
167.13/42.62	     b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(b(c(x1))) -> a#(x1)
167.13/42.62	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(b(x1))))
167.13/42.62	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
167.13/42.62	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
167.13/42.62	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
167.13/42.62	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
167.13/42.62	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
167.13/42.62	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
167.13/42.62	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
167.13/42.62	    SCC Processor:
167.13/42.62	     #sccs: 1
167.13/42.62	     #rules: 2
167.13/42.62	     #arcs: 9/25
167.13/42.62	     DPs:
167.13/42.62	      b#(a(x1)) -> b#(b(x1))
167.13/42.62	      b#(a(x1)) -> b#(x1)
167.13/42.62	     TRS:
167.13/42.62	      a(x1) -> x1
167.13/42.62	      b(a(x1)) -> c(a(b(b(x1))))
167.13/42.62	      b(x1) -> x1
167.13/42.62	      c(b(c(x1))) -> a(x1)
167.13/42.62	     Arctic Interpretation Processor:
167.13/42.62	      dimension: 2
167.13/42.62	      usable rules:
167.13/42.62	       a(x1) -> x1
167.13/42.62	       b(a(x1)) -> c(a(b(b(x1))))
167.13/42.62	       b(x1) -> x1
167.13/42.62	       c(b(c(x1))) -> a(x1)
167.13/42.62	      interpretation:
167.13/42.62	       [b#](x0) = [0 0]x0,
167.13/42.62	       
167.13/42.62	                 [0 0]     [0]
167.13/42.62	       [c](x0) = [1 0]x0 + [0],
167.13/42.62	       
167.13/42.62	                 [0 0]  
167.13/42.62	       [b](x0) = [0 0]x0,
167.13/42.62	       
167.13/42.62	                 [0 0]     [-&]
167.13/42.62	       [a](x0) = [1 1]x0 + [0 ]
167.13/42.62	      orientation:
167.13/42.62	       b#(a(x1)) = [1 1]x1 + [0] >= [0 0]x1 = b#(b(x1))
167.13/42.62	       
167.13/42.62	       b#(a(x1)) = [1 1]x1 + [0] >= [0 0]x1 = b#(x1)
167.13/42.62	       
167.13/42.62	               [0 0]     [-&]           
167.13/42.62	       a(x1) = [1 1]x1 + [0 ] >= x1 = x1
167.13/42.62	       
167.13/42.62	                  [1 1]     [0]    [1 1]     [0]                 
167.13/42.62	       b(a(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = c(a(b(b(x1))))
167.13/42.62	       
167.13/42.62	               [0 0]             
167.13/42.62	       b(x1) = [0 0]x1 >= x1 = x1
167.13/42.62	       
167.13/42.62	                     [1 0]     [0]    [0 0]     [-&]        
167.13/42.62	       c(b(c(x1))) = [2 1]x1 + [1] >= [1 1]x1 + [0 ] = a(x1)
167.13/42.62	      problem:
167.13/42.62	       DPs:
167.13/42.62	        
167.13/42.62	       TRS:
167.13/42.62	        a(x1) -> x1
167.13/42.62	        b(a(x1)) -> c(a(b(b(x1))))
167.13/42.62	        b(x1) -> x1
167.13/42.62	        c(b(c(x1))) -> a(x1)
167.13/42.62	      Qed
167.13/42.62	EOF