176.15/43.55	YES
176.45/43.55	
176.45/43.55	Problem:
176.45/43.55	 a(b(x1)) -> x1
176.45/43.55	 a(b(x1)) -> b(c(x1))
176.45/43.55	 a(c(x1)) -> c(b(a(a(x1))))
176.45/43.55	
176.45/43.55	Proof:
176.45/43.55	 String Reversal Processor:
176.45/43.55	  b(a(x1)) -> x1
176.45/43.55	  b(a(x1)) -> c(b(x1))
176.45/43.55	  c(a(x1)) -> a(a(b(c(x1))))
176.45/43.55	  DP Processor:
176.45/43.55	   DPs:
176.45/43.55	    b#(a(x1)) -> b#(x1)
176.45/43.55	    b#(a(x1)) -> c#(b(x1))
176.45/43.55	    c#(a(x1)) -> c#(x1)
176.45/43.55	    c#(a(x1)) -> b#(c(x1))
176.45/43.55	   TRS:
176.45/43.55	    b(a(x1)) -> x1
176.45/43.55	    b(a(x1)) -> c(b(x1))
176.45/43.55	    c(a(x1)) -> a(a(b(c(x1))))
176.45/43.55	   TDG Processor:
176.45/43.55	    DPs:
176.45/43.55	     b#(a(x1)) -> b#(x1)
176.45/43.55	     b#(a(x1)) -> c#(b(x1))
176.45/43.55	     c#(a(x1)) -> c#(x1)
176.45/43.55	     c#(a(x1)) -> b#(c(x1))
176.45/43.55	    TRS:
176.45/43.55	     b(a(x1)) -> x1
176.45/43.55	     b(a(x1)) -> c(b(x1))
176.45/43.55	     c(a(x1)) -> a(a(b(c(x1))))
176.45/43.55	    graph:
176.45/43.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(x1))
176.45/43.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
176.45/43.55	     c#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(x1))
176.45/43.55	     c#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(x1)
176.45/43.55	     b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> b#(c(x1))
176.45/43.55	     b#(a(x1)) -> c#(b(x1)) -> c#(a(x1)) -> c#(x1)
176.45/43.55	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
176.45/43.55	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
176.45/43.55	    Arctic Interpretation Processor:
176.45/43.55	     dimension: 2
176.45/43.55	     usable rules:
176.45/43.55	      b(a(x1)) -> x1
176.45/43.55	      b(a(x1)) -> c(b(x1))
176.45/43.55	      c(a(x1)) -> a(a(b(c(x1))))
176.45/43.55	     interpretation:
176.45/43.55	      [c#](x0) = [0 1]x0 + [0],
176.45/43.55	      
176.45/43.55	      [b#](x0) = [-& 0 ]x0 + [0],
176.45/43.55	      
176.45/43.55	                [-& -&]     [0 ]
176.45/43.55	      [c](x0) = [-& 1 ]x0 + [-&],
176.45/43.55	      
176.45/43.55	                [-& -&]     [0]
176.45/43.55	      [a](x0) = [1  1 ]x0 + [3],
176.45/43.55	      
176.45/43.55	                [0  -1]     [-4]
176.45/43.55	      [b](x0) = [-& -1]x0 + [-1]
176.45/43.55	     orientation:
176.45/43.55	      b#(a(x1)) = [1 1]x1 + [3] >= [-& 0 ]x1 + [0] = b#(x1)
176.45/43.55	      
176.45/43.55	      b#(a(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [0] = c#(b(x1))
176.45/43.55	      
176.45/43.55	      c#(a(x1)) = [2 2]x1 + [4] >= [0 1]x1 + [0] = c#(x1)
176.45/43.55	      
176.45/43.55	      c#(a(x1)) = [2 2]x1 + [4] >= [-& 1 ]x1 + [0] = b#(c(x1))
176.45/43.55	      
176.45/43.55	                 [0 0]     [2]           
176.45/43.55	      b(a(x1)) = [0 0]x1 + [2] >= x1 = x1
176.45/43.55	      
176.45/43.55	                 [0 0]     [2]    [-& -&]     [0]           
176.45/43.55	      b(a(x1)) = [0 0]x1 + [2] >= [-& 0 ]x1 + [0] = c(b(x1))
176.45/43.55	      
176.45/43.55	                 [-& -&]     [0]    [-& -&]     [0]                 
176.45/43.55	      c(a(x1)) = [2  2 ]x1 + [4] >= [-& 2 ]x1 + [4] = a(a(b(c(x1))))
176.45/43.55	     problem:
176.45/43.55	      DPs:
176.45/43.55	       
176.45/43.55	      TRS:
176.45/43.55	       b(a(x1)) -> x1
176.45/43.55	       b(a(x1)) -> c(b(x1))
176.45/43.55	       c(a(x1)) -> a(a(b(c(x1))))
176.45/43.55	     Qed
176.45/43.55	EOF