169.04/43.17	YES
169.04/43.18	
169.04/43.18	Problem:
169.04/43.18	 a(x1) -> x1
169.04/43.18	 a(x1) -> b(b(x1))
169.04/43.18	 a(b(x1)) -> a(c(a(c(x1))))
169.04/43.18	 c(c(x1)) -> x1
169.04/43.18	
169.04/43.18	Proof:
169.04/43.18	 String Reversal Processor:
169.04/43.18	  a(x1) -> x1
169.04/43.18	  a(x1) -> b(b(x1))
169.04/43.18	  b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	  c(c(x1)) -> x1
169.04/43.18	  DP Processor:
169.04/43.18	   DPs:
169.04/43.18	    a#(x1) -> b#(x1)
169.04/43.18	    a#(x1) -> b#(b(x1))
169.04/43.18	    b#(a(x1)) -> c#(a(x1))
169.04/43.18	    b#(a(x1)) -> a#(c(a(x1)))
169.04/43.18	    b#(a(x1)) -> c#(a(c(a(x1))))
169.04/43.18	   TRS:
169.04/43.18	    a(x1) -> x1
169.04/43.18	    a(x1) -> b(b(x1))
169.04/43.18	    b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	    c(c(x1)) -> x1
169.04/43.18	   TDG Processor:
169.04/43.18	    DPs:
169.04/43.18	     a#(x1) -> b#(x1)
169.04/43.18	     a#(x1) -> b#(b(x1))
169.04/43.18	     b#(a(x1)) -> c#(a(x1))
169.04/43.18	     b#(a(x1)) -> a#(c(a(x1)))
169.04/43.18	     b#(a(x1)) -> c#(a(c(a(x1))))
169.04/43.18	    TRS:
169.04/43.18	     a(x1) -> x1
169.04/43.18	     a(x1) -> b(b(x1))
169.04/43.18	     b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	     c(c(x1)) -> x1
169.04/43.18	    graph:
169.04/43.18	     b#(a(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(b(x1))
169.04/43.18	     b#(a(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(x1)
169.04/43.18	     a#(x1) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(c(a(x1))))
169.04/43.18	     a#(x1) -> b#(b(x1)) -> b#(a(x1)) -> a#(c(a(x1)))
169.04/43.18	     a#(x1) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(x1))
169.04/43.18	     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(c(a(x1))))
169.04/43.18	     a#(x1) -> b#(x1) -> b#(a(x1)) -> a#(c(a(x1)))
169.04/43.18	     a#(x1) -> b#(x1) -> b#(a(x1)) -> c#(a(x1))
169.04/43.18	    SCC Processor:
169.04/43.18	     #sccs: 1
169.04/43.18	     #rules: 3
169.04/43.18	     #arcs: 8/25
169.04/43.18	     DPs:
169.04/43.18	      b#(a(x1)) -> a#(c(a(x1)))
169.04/43.18	      a#(x1) -> b#(x1)
169.04/43.18	      a#(x1) -> b#(b(x1))
169.04/43.18	     TRS:
169.04/43.18	      a(x1) -> x1
169.04/43.18	      a(x1) -> b(b(x1))
169.04/43.18	      b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	      c(c(x1)) -> x1
169.04/43.18	     Arctic Interpretation Processor:
169.04/43.18	      dimension: 2
169.04/43.18	      usable rules:
169.04/43.18	       a(x1) -> x1
169.04/43.18	       a(x1) -> b(b(x1))
169.04/43.18	       b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	       c(c(x1)) -> x1
169.04/43.18	      interpretation:
169.04/43.18	       [b#](x0) = [1 0]x0,
169.04/43.18	       
169.04/43.18	       [a#](x0) = [1 0]x0 + [0],
169.04/43.18	       
169.04/43.18	                 [-& 0 ]     [0]
169.04/43.18	       [c](x0) = [0  0 ]x0 + [0],
169.04/43.18	       
169.04/43.18	                 [0  -&]     [-&]
169.04/43.18	       [b](x0) = [1  0 ]x0 + [0 ],
169.04/43.18	       
169.04/43.18	                 [2 1]     [3]
169.04/43.18	       [a](x0) = [1 0]x0 + [0]
169.04/43.18	      orientation:
169.04/43.18	       b#(a(x1)) = [3 2]x1 + [4] >= [2 1]x1 + [3] = a#(c(a(x1)))
169.04/43.18	       
169.04/43.18	       a#(x1) = [1 0]x1 + [0] >= [1 0]x1 = b#(x1)
169.04/43.18	       
169.04/43.18	       a#(x1) = [1 0]x1 + [0] >= [1 0]x1 + [0] = b#(b(x1))
169.04/43.18	       
169.04/43.18	               [2 1]     [3]           
169.04/43.18	       a(x1) = [1 0]x1 + [0] >= x1 = x1
169.04/43.18	       
169.04/43.18	               [2 1]     [3]    [0  -&]     [-&]           
169.04/43.18	       a(x1) = [1 0]x1 + [0] >= [1  0 ]x1 + [0 ] = b(b(x1))
169.04/43.18	       
169.04/43.18	                  [2 1]     [3]    [2 1]     [3]                 
169.04/43.18	       b(a(x1)) = [3 2]x1 + [4] >= [3 2]x1 + [4] = c(a(c(a(x1))))
169.04/43.18	       
169.04/43.18	                  [0 0]     [0]           
169.04/43.18	       c(c(x1)) = [0 0]x1 + [0] >= x1 = x1
169.04/43.18	      problem:
169.04/43.18	       DPs:
169.04/43.18	        a#(x1) -> b#(x1)
169.04/43.18	        a#(x1) -> b#(b(x1))
169.04/43.18	       TRS:
169.04/43.18	        a(x1) -> x1
169.04/43.18	        a(x1) -> b(b(x1))
169.04/43.18	        b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	        c(c(x1)) -> x1
169.04/43.18	      Restore Modifier:
169.04/43.18	       DPs:
169.04/43.18	        a#(x1) -> b#(x1)
169.04/43.18	        a#(x1) -> b#(b(x1))
169.04/43.18	       TRS:
169.04/43.18	        a(x1) -> x1
169.04/43.18	        a(x1) -> b(b(x1))
169.04/43.18	        b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	        c(c(x1)) -> x1
169.04/43.18	       EDG Processor:
169.04/43.18	        DPs:
169.04/43.18	         a#(x1) -> b#(x1)
169.04/43.18	         a#(x1) -> b#(b(x1))
169.04/43.18	        TRS:
169.04/43.18	         a(x1) -> x1
169.04/43.18	         a(x1) -> b(b(x1))
169.04/43.18	         b(a(x1)) -> c(a(c(a(x1))))
169.04/43.18	         c(c(x1)) -> x1
169.04/43.18	        graph:
169.04/43.18	         
169.04/43.18	        SCC Processor:
169.04/43.18	         #sccs: 0
169.04/43.18	         #rules: 0
169.04/43.18	         #arcs: 0/4
169.04/43.18	         
169.04/43.18	EOF