173.92/44.87	YES
173.92/44.88	
173.92/44.88	Problem:
173.92/44.88	 a(a(x1)) -> a(b(c(b(x1))))
173.92/44.88	 b(c(x1)) -> x1
173.92/44.88	 c(b(x1)) -> a(c(x1))
173.92/44.88	
173.92/44.88	Proof:
173.92/44.88	 String Reversal Processor:
173.92/44.88	  a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	  c(b(x1)) -> x1
173.92/44.88	  b(c(x1)) -> c(a(x1))
173.92/44.88	  DP Processor:
173.92/44.88	   DPs:
173.92/44.88	    a#(a(x1)) -> b#(a(x1))
173.92/44.88	    a#(a(x1)) -> c#(b(a(x1)))
173.92/44.88	    a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	    b#(c(x1)) -> a#(x1)
173.92/44.88	    b#(c(x1)) -> c#(a(x1))
173.92/44.88	   TRS:
173.92/44.88	    a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	    c(b(x1)) -> x1
173.92/44.88	    b(c(x1)) -> c(a(x1))
173.92/44.88	   TDG Processor:
173.92/44.88	    DPs:
173.92/44.88	     a#(a(x1)) -> b#(a(x1))
173.92/44.88	     a#(a(x1)) -> c#(b(a(x1)))
173.92/44.88	     a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	     b#(c(x1)) -> a#(x1)
173.92/44.88	     b#(c(x1)) -> c#(a(x1))
173.92/44.88	    TRS:
173.92/44.88	     a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	     c(b(x1)) -> x1
173.92/44.88	     b(c(x1)) -> c(a(x1))
173.92/44.88	    graph:
173.92/44.88	     b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	     b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(a(x1)))
173.92/44.88	     b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
173.92/44.88	     a#(a(x1)) -> b#(c(b(a(x1)))) -> b#(c(x1)) -> c#(a(x1))
173.92/44.88	     a#(a(x1)) -> b#(c(b(a(x1)))) -> b#(c(x1)) -> a#(x1)
173.92/44.88	     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> c#(a(x1))
173.92/44.88	     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
173.92/44.88	    SCC Processor:
173.92/44.88	     #sccs: 1
173.92/44.88	     #rules: 3
173.92/44.88	     #arcs: 7/25
173.92/44.88	     DPs:
173.92/44.88	      b#(c(x1)) -> a#(x1)
173.92/44.88	      a#(a(x1)) -> b#(a(x1))
173.92/44.88	      a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	     TRS:
173.92/44.88	      a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	      c(b(x1)) -> x1
173.92/44.88	      b(c(x1)) -> c(a(x1))
173.92/44.88	     Arctic Interpretation Processor:
173.92/44.88	      dimension: 2
173.92/44.88	      usable rules:
173.92/44.88	       a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	       c(b(x1)) -> x1
173.92/44.88	       b(c(x1)) -> c(a(x1))
173.92/44.88	      interpretation:
173.92/44.88	       [b#](x0) = [2 1]x0 + [3],
173.92/44.88	       
173.92/44.88	       [a#](x0) = [0 1]x0,
173.92/44.88	       
173.92/44.88	                 [-& 0 ]     [0]
173.92/44.88	       [c](x0) = [0  -&]x0 + [0],
173.92/44.88	       
173.92/44.88	                 [1  0 ]     [2]
173.92/44.88	       [b](x0) = [0  -&]x0 + [0],
173.92/44.88	       
173.92/44.88	                 [-& 0 ]     [0]
173.92/44.88	       [a](x0) = [0  1 ]x0 + [2]
173.92/44.88	      orientation:
173.92/44.88	       b#(c(x1)) = [1 2]x1 + [3] >= [0 1]x1 = a#(x1)
173.92/44.88	       
173.92/44.88	       a#(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = b#(a(x1))
173.92/44.88	       
173.92/44.88	       a#(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = b#(c(b(a(x1))))
173.92/44.88	       
173.92/44.88	                  [0 1]     [2]    [0  1 ]     [2]                 
173.92/44.88	       a(a(x1)) = [1 2]x1 + [3] >= [-& 0 ]x1 + [0] = b(c(b(a(x1))))
173.92/44.88	       
173.92/44.88	                  [0  -&]     [0]           
173.92/44.88	       c(b(x1)) = [1  0 ]x1 + [2] >= x1 = x1
173.92/44.88	       
173.92/44.88	                  [0  1 ]     [2]    [0  1 ]     [2]           
173.92/44.88	       b(c(x1)) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = c(a(x1))
173.92/44.88	      problem:
173.92/44.88	       DPs:
173.92/44.88	        a#(a(x1)) -> b#(a(x1))
173.92/44.88	        a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	       TRS:
173.92/44.88	        a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	        c(b(x1)) -> x1
173.92/44.88	        b(c(x1)) -> c(a(x1))
173.92/44.88	      Restore Modifier:
173.92/44.88	       DPs:
173.92/44.88	        a#(a(x1)) -> b#(a(x1))
173.92/44.88	        a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	       TRS:
173.92/44.88	        a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	        c(b(x1)) -> x1
173.92/44.88	        b(c(x1)) -> c(a(x1))
173.92/44.88	       EDG Processor:
173.92/44.88	        DPs:
173.92/44.88	         a#(a(x1)) -> b#(a(x1))
173.92/44.88	         a#(a(x1)) -> b#(c(b(a(x1))))
173.92/44.88	        TRS:
173.92/44.88	         a(a(x1)) -> b(c(b(a(x1))))
173.92/44.88	         c(b(x1)) -> x1
173.92/44.88	         b(c(x1)) -> c(a(x1))
173.92/44.88	        graph:
173.92/44.88	         
173.92/44.88	        SCC Processor:
173.92/44.88	         #sccs: 0
173.92/44.88	         #rules: 0
173.92/44.88	         #arcs: 0/4
173.92/44.88	         
173.92/44.88	EOF