191.03/48.39	YES
191.03/48.40	
191.03/48.40	Problem:
191.03/48.40	 a(x1) -> x1
191.03/48.40	 a(a(b(b(x1)))) -> b(c(a(c(x1))))
191.03/48.40	 c(x1) -> b(a(x1))
191.03/48.40	
191.03/48.40	Proof:
191.03/48.40	 String Reversal Processor:
191.03/48.40	  a(x1) -> x1
191.03/48.40	  b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	  c(x1) -> a(b(x1))
191.03/48.40	  DP Processor:
191.03/48.40	   DPs:
191.03/48.40	    b#(b(a(a(x1)))) -> b#(x1)
191.03/48.40	    b#(b(a(a(x1)))) -> c#(b(x1))
191.03/48.40	    b#(b(a(a(x1)))) -> a#(c(b(x1)))
191.03/48.40	    b#(b(a(a(x1)))) -> c#(a(c(b(x1))))
191.03/48.40	    c#(x1) -> b#(x1)
191.03/48.40	    c#(x1) -> a#(b(x1))
191.03/48.40	   TRS:
191.03/48.40	    a(x1) -> x1
191.03/48.40	    b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	    c(x1) -> a(b(x1))
191.03/48.40	   TDG Processor:
191.03/48.40	    DPs:
191.03/48.40	     b#(b(a(a(x1)))) -> b#(x1)
191.03/48.40	     b#(b(a(a(x1)))) -> c#(b(x1))
191.03/48.40	     b#(b(a(a(x1)))) -> a#(c(b(x1)))
191.03/48.40	     b#(b(a(a(x1)))) -> c#(a(c(b(x1))))
191.03/48.40	     c#(x1) -> b#(x1)
191.03/48.40	     c#(x1) -> a#(b(x1))
191.03/48.40	    TRS:
191.03/48.40	     a(x1) -> x1
191.03/48.40	     b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	     c(x1) -> a(b(x1))
191.03/48.40	    graph:
191.03/48.40	     c#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(a(c(b(x1))))
191.03/48.40	     c#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(c(b(x1)))
191.03/48.40	     c#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(b(x1))
191.03/48.40	     c#(x1) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1)
191.03/48.40	     b#(b(a(a(x1)))) -> c#(b(x1)) -> c#(x1) -> a#(b(x1))
191.03/48.40	     b#(b(a(a(x1)))) -> c#(b(x1)) -> c#(x1) -> b#(x1)
191.03/48.40	     b#(b(a(a(x1)))) -> c#(a(c(b(x1)))) -> c#(x1) -> a#(b(x1))
191.03/48.40	     b#(b(a(a(x1)))) -> c#(a(c(b(x1)))) -> c#(x1) -> b#(x1)
191.03/48.40	     b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(a(c(b(x1))))
191.03/48.40	     b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(c(b(x1)))
191.03/48.40	     b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> c#(b(x1))
191.03/48.40	     b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1)
191.03/48.40	    SCC Processor:
191.03/48.40	     #sccs: 1
191.03/48.40	     #rules: 4
191.03/48.40	     #arcs: 12/36
191.03/48.40	     DPs:
191.03/48.40	      c#(x1) -> b#(x1)
191.03/48.40	      b#(b(a(a(x1)))) -> b#(x1)
191.03/48.40	      b#(b(a(a(x1)))) -> c#(b(x1))
191.03/48.40	      b#(b(a(a(x1)))) -> c#(a(c(b(x1))))
191.03/48.40	     TRS:
191.03/48.40	      a(x1) -> x1
191.03/48.40	      b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	      c(x1) -> a(b(x1))
191.03/48.40	     Arctic Interpretation Processor:
191.03/48.40	      dimension: 4
191.03/48.40	      usable rules:
191.03/48.40	       a(x1) -> x1
191.03/48.40	       b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	       c(x1) -> a(b(x1))
191.03/48.40	      interpretation:
191.03/48.40	       [c#](x0) = [-& 0  -& -&]x0 + [0],
191.03/48.40	       
191.03/48.40	       [b#](x0) = [-& 0  -& -&]x0 + [0],
191.03/48.40	       
191.03/48.40	                 [0  1  0  0 ]     [1]
191.03/48.40	                 [0  0  0  0 ]     [0]
191.03/48.40	       [c](x0) = [0  0  0  0 ]x0 + [0]
191.03/48.40	                 [0  1  0  -&]     [1],
191.03/48.40	       
191.03/48.40	                 [0  0  -& -&]     [-&]
191.03/48.40	                 [0  0  0  0 ]     [0 ]
191.03/48.40	       [b](x0) = [-& 0  -& -&]x0 + [0 ]
191.03/48.40	                 [0  0  0  -&]     [0 ],
191.03/48.40	       
191.03/48.40	                 [0  0  1  0 ]     [1]
191.03/48.40	                 [-& 0  0  -&]     [0]
191.03/48.40	       [a](x0) = [0  0  0  0 ]x0 + [0]
191.03/48.40	                 [0  -& 0  0 ]     [0]
191.03/48.40	      orientation:
191.03/48.40	       c#(x1) = [-& 0  -& -&]x1 + [0] >= [-& 0  -& -&]x1 + [0] = b#(x1)
191.03/48.40	       
191.03/48.40	       b#(b(a(a(x1)))) = [1 1 1 1]x1 + [1] >= [-& 0  -& -&]x1 + [0] = b#(x1)
191.03/48.40	       
191.03/48.40	       b#(b(a(a(x1)))) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = c#(b(x1))
191.03/48.40	       
191.03/48.40	       b#(b(a(a(x1)))) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = c#(a(c(b(x1))))
191.03/48.40	       
191.03/48.40	               [0  0  1  0 ]     [1]           
191.03/48.40	               [-& 0  0  -&]     [0]           
191.03/48.40	       a(x1) = [0  0  0  0 ]x1 + [0] >= x1 = x1
191.03/48.40	               [0  -& 0  0 ]     [0]           
191.03/48.40	       
191.03/48.40	                        [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
191.03/48.40	                        [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
191.03/48.40	       b(b(a(a(x1)))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = c(a(c(b(x1))))
191.03/48.40	                        [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
191.03/48.40	       
191.03/48.40	               [0  1  0  0 ]     [1]    [0  1  0  0 ]     [1]           
191.03/48.40	               [0  0  0  0 ]     [0]    [0  0  0  0 ]     [0]           
191.03/48.40	       c(x1) = [0  0  0  0 ]x1 + [0] >= [0  0  0  0 ]x1 + [0] = a(b(x1))
191.03/48.40	               [0  1  0  -&]     [1]    [0  0  0  -&]     [0]           
191.03/48.40	      problem:
191.03/48.40	       DPs:
191.03/48.40	        c#(x1) -> b#(x1)
191.03/48.40	       TRS:
191.03/48.40	        a(x1) -> x1
191.03/48.40	        b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	        c(x1) -> a(b(x1))
191.03/48.40	      Restore Modifier:
191.03/48.40	       DPs:
191.03/48.40	        c#(x1) -> b#(x1)
191.03/48.40	       TRS:
191.03/48.40	        a(x1) -> x1
191.03/48.40	        b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	        c(x1) -> a(b(x1))
191.03/48.40	       EDG Processor:
191.03/48.40	        DPs:
191.03/48.40	         c#(x1) -> b#(x1)
191.03/48.40	        TRS:
191.03/48.40	         a(x1) -> x1
191.03/48.40	         b(b(a(a(x1)))) -> c(a(c(b(x1))))
191.03/48.40	         c(x1) -> a(b(x1))
191.03/48.40	        graph:
191.03/48.40	         
191.03/48.40	        SCC Processor:
191.03/48.40	         #sccs: 0
191.03/48.40	         #rules: 0
191.03/48.40	         #arcs: 0/1
191.03/48.40	         
191.03/48.41	EOF