168.47/43.04	YES
168.47/43.05	
168.47/43.05	Problem:
168.47/43.05	 a(x1) -> x1
168.47/43.05	 a(b(x1)) -> x1
168.47/43.05	 b(a(x1)) -> a(a(b(c(x1))))
168.47/43.05	 c(c(x1)) -> b(x1)
168.47/43.05	
168.47/43.05	Proof:
168.47/43.05	 String Reversal Processor:
168.47/43.05	  a(x1) -> x1
168.47/43.05	  b(a(x1)) -> x1
168.47/43.05	  a(b(x1)) -> c(b(a(a(x1))))
168.47/43.05	  c(c(x1)) -> b(x1)
168.47/43.05	  DP Processor:
168.47/43.05	   DPs:
168.47/43.05	    a#(b(x1)) -> a#(x1)
168.47/43.05	    a#(b(x1)) -> a#(a(x1))
168.47/43.05	    a#(b(x1)) -> b#(a(a(x1)))
168.47/43.05	    a#(b(x1)) -> c#(b(a(a(x1))))
168.47/43.05	    c#(c(x1)) -> b#(x1)
168.47/43.05	   TRS:
168.47/43.05	    a(x1) -> x1
168.47/43.05	    b(a(x1)) -> x1
168.47/43.05	    a(b(x1)) -> c(b(a(a(x1))))
168.47/43.05	    c(c(x1)) -> b(x1)
168.47/43.05	   TDG Processor:
168.47/43.05	    DPs:
168.47/43.05	     a#(b(x1)) -> a#(x1)
168.47/43.05	     a#(b(x1)) -> a#(a(x1))
168.47/43.05	     a#(b(x1)) -> b#(a(a(x1)))
168.47/43.05	     a#(b(x1)) -> c#(b(a(a(x1))))
168.47/43.05	     c#(c(x1)) -> b#(x1)
168.47/43.05	    TRS:
168.47/43.05	     a(x1) -> x1
168.47/43.05	     b(a(x1)) -> x1
168.47/43.05	     a(b(x1)) -> c(b(a(a(x1))))
168.47/43.05	     c(c(x1)) -> b(x1)
168.47/43.05	    graph:
168.47/43.05	     a#(b(x1)) -> c#(b(a(a(x1)))) -> c#(c(x1)) -> b#(x1)
168.47/43.05	     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> c#(b(a(a(x1))))
168.47/43.05	     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
168.47/43.05	     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
168.47/43.05	     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
168.47/43.05	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(a(a(x1))))
168.47/43.05	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
168.47/43.05	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
168.47/43.05	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
168.47/43.05	    SCC Processor:
168.47/43.05	     #sccs: 1
168.47/43.05	     #rules: 2
168.47/43.05	     #arcs: 9/25
168.47/43.05	     DPs:
168.47/43.05	      a#(b(x1)) -> a#(a(x1))
168.47/43.05	      a#(b(x1)) -> a#(x1)
168.47/43.05	     TRS:
168.47/43.05	      a(x1) -> x1
168.47/43.05	      b(a(x1)) -> x1
168.47/43.05	      a(b(x1)) -> c(b(a(a(x1))))
168.47/43.05	      c(c(x1)) -> b(x1)
168.47/43.05	     Arctic Interpretation Processor:
168.47/43.05	      dimension: 2
168.47/43.05	      usable rules:
168.47/43.05	       a(x1) -> x1
168.47/43.05	       b(a(x1)) -> x1
168.47/43.05	       a(b(x1)) -> c(b(a(a(x1))))
168.47/43.05	       c(c(x1)) -> b(x1)
168.47/43.05	      interpretation:
168.47/43.05	       [a#](x0) = [0 0]x0 + [0],
168.47/43.05	       
168.47/43.05	                 [-& 1 ]     [0]
168.47/43.05	       [c](x0) = [0  1 ]x0 + [3],
168.47/43.05	       
168.47/43.05	                 [1 1]     [3 ]
168.47/43.05	       [b](x0) = [0 0]x0 + [-&],
168.47/43.05	       
168.47/43.05	                 [0 0]     [-&]
168.47/43.05	       [a](x0) = [0 0]x0 + [2 ]
168.47/43.05	      orientation:
168.47/43.05	       a#(b(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [2] = a#(a(x1))
168.47/43.05	       
168.47/43.05	       a#(b(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [0] = a#(x1)
168.47/43.05	       
168.47/43.05	               [0 0]     [-&]           
168.47/43.05	       a(x1) = [0 0]x1 + [2 ] >= x1 = x1
168.47/43.05	       
168.47/43.05	                  [1 1]     [3]           
168.47/43.05	       b(a(x1)) = [0 0]x1 + [2] >= x1 = x1
168.47/43.05	       
168.47/43.05	                  [1 1]     [3]    [1 1]     [3]                 
168.47/43.05	       a(b(x1)) = [1 1]x1 + [3] >= [1 1]x1 + [3] = c(b(a(a(x1))))
168.47/43.05	       
168.47/43.05	                  [1 2]     [4]    [1 1]     [3 ]        
168.47/43.05	       c(c(x1)) = [1 2]x1 + [4] >= [0 0]x1 + [-&] = b(x1)
168.47/43.05	      problem:
168.47/43.05	       DPs:
168.47/43.05	        
168.47/43.05	       TRS:
168.47/43.05	        a(x1) -> x1
168.47/43.05	        b(a(x1)) -> x1
168.47/43.05	        a(b(x1)) -> c(b(a(a(x1))))
168.47/43.05	        c(c(x1)) -> b(x1)
168.47/43.05	      Qed
168.47/43.05	EOF