167.93/42.95	YES
167.93/42.95	
167.93/42.95	Problem:
167.93/42.95	 a(x1) -> x1
167.93/42.95	 a(b(x1)) -> b(b(c(a(x1))))
167.93/42.95	 b(b(x1)) -> a(x1)
167.93/42.95	 c(c(x1)) -> x1
167.93/42.95	
167.93/42.95	Proof:
167.93/42.95	 String Reversal Processor:
167.93/42.95	  a(x1) -> x1
167.93/42.95	  b(a(x1)) -> a(c(b(b(x1))))
167.93/42.95	  b(b(x1)) -> a(x1)
167.93/42.95	  c(c(x1)) -> x1
167.93/42.95	  DP Processor:
167.93/42.95	   DPs:
167.93/42.95	    b#(a(x1)) -> b#(x1)
167.93/42.95	    b#(a(x1)) -> b#(b(x1))
167.93/42.95	    b#(a(x1)) -> c#(b(b(x1)))
167.93/42.95	    b#(a(x1)) -> a#(c(b(b(x1))))
167.93/42.95	    b#(b(x1)) -> a#(x1)
167.93/42.95	   TRS:
167.93/42.95	    a(x1) -> x1
167.93/42.95	    b(a(x1)) -> a(c(b(b(x1))))
167.93/42.95	    b(b(x1)) -> a(x1)
167.93/42.95	    c(c(x1)) -> x1
167.93/42.95	   TDG Processor:
167.93/42.95	    DPs:
167.93/42.95	     b#(a(x1)) -> b#(x1)
167.93/42.95	     b#(a(x1)) -> b#(b(x1))
167.93/42.95	     b#(a(x1)) -> c#(b(b(x1)))
167.93/42.95	     b#(a(x1)) -> a#(c(b(b(x1))))
167.93/42.95	     b#(b(x1)) -> a#(x1)
167.93/42.95	    TRS:
167.93/42.95	     a(x1) -> x1
167.93/42.95	     b(a(x1)) -> a(c(b(b(x1))))
167.93/42.95	     b(b(x1)) -> a(x1)
167.93/42.95	     c(c(x1)) -> x1
167.93/42.95	    graph:
167.93/42.95	     b#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> a#(x1)
167.93/42.95	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(b(b(x1))))
167.93/42.95	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(b(b(x1)))
167.93/42.95	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
167.93/42.95	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
167.93/42.95	     b#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1)
167.93/42.95	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(b(b(x1))))
167.93/42.95	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(b(x1)))
167.93/42.95	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
167.93/42.95	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
167.93/42.95	    SCC Processor:
167.93/42.95	     #sccs: 1
167.93/42.95	     #rules: 2
167.93/42.95	     #arcs: 10/25
167.93/42.95	     DPs:
167.93/42.95	      b#(a(x1)) -> b#(b(x1))
167.93/42.95	      b#(a(x1)) -> b#(x1)
167.93/42.95	     TRS:
167.93/42.95	      a(x1) -> x1
167.93/42.95	      b(a(x1)) -> a(c(b(b(x1))))
167.93/42.95	      b(b(x1)) -> a(x1)
167.93/42.95	      c(c(x1)) -> x1
167.93/42.95	     Arctic Interpretation Processor:
167.93/42.95	      dimension: 2
167.93/42.95	      usable rules:
167.93/42.95	       a(x1) -> x1
167.93/42.95	       b(a(x1)) -> a(c(b(b(x1))))
167.93/42.95	       b(b(x1)) -> a(x1)
167.93/42.95	       c(c(x1)) -> x1
167.93/42.95	      interpretation:
167.93/42.95	       [b#](x0) = [3 3]x0 + [0],
167.93/42.95	       
167.93/42.95	                 [-& 0 ]     [0]
167.93/42.95	       [c](x0) = [0  0 ]x0 + [0],
167.93/42.95	       
167.93/42.95	                 [1 0]     [2]
167.93/42.95	       [b](x0) = [0 0]x0 + [0],
167.93/42.95	       
167.93/42.95	                 [2 1]     [3]
167.93/42.95	       [a](x0) = [0 0]x0 + [2]
167.93/42.95	      orientation:
167.93/42.95	       b#(a(x1)) = [5 4]x1 + [6] >= [4 3]x1 + [5] = b#(b(x1))
167.93/42.95	       
167.93/42.95	       b#(a(x1)) = [5 4]x1 + [6] >= [3 3]x1 + [0] = b#(x1)
167.93/42.95	       
167.93/42.95	               [2 1]     [3]           
167.93/42.95	       a(x1) = [0 0]x1 + [2] >= x1 = x1
167.93/42.95	       
167.93/42.95	                  [3 2]     [4]    [3 2]     [4]                 
167.93/42.95	       b(a(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a(c(b(b(x1))))
167.93/42.95	       
167.93/42.95	                  [2 1]     [3]    [2 1]     [3]        
167.93/42.95	       b(b(x1)) = [1 0]x1 + [2] >= [0 0]x1 + [2] = a(x1)
167.93/42.95	       
167.93/42.95	                  [0 0]     [0]           
167.93/42.95	       c(c(x1)) = [0 0]x1 + [0] >= x1 = x1
167.93/42.95	      problem:
167.93/42.95	       DPs:
167.93/42.95	        
167.93/42.95	       TRS:
167.93/42.95	        a(x1) -> x1
167.93/42.95	        b(a(x1)) -> a(c(b(b(x1))))
167.93/42.95	        b(b(x1)) -> a(x1)
167.93/42.95	        c(c(x1)) -> x1
167.93/42.95	      Qed
167.93/42.96	EOF