171.08/43.71	YES
171.08/43.72	
171.08/43.72	Problem:
171.08/43.72	 a(x1) -> b(x1)
171.08/43.72	 a(c(x1)) -> c(c(a(a(b(x1)))))
171.08/43.72	 b(b(x1)) -> x1
171.08/43.72	
171.08/43.72	Proof:
171.08/43.72	 String Reversal Processor:
171.08/43.72	  a(x1) -> b(x1)
171.08/43.72	  c(a(x1)) -> b(a(a(c(c(x1)))))
171.08/43.72	  b(b(x1)) -> x1
171.08/43.72	  DP Processor:
171.08/43.72	   DPs:
171.08/43.72	    a#(x1) -> b#(x1)
171.08/43.72	    c#(a(x1)) -> c#(x1)
171.08/43.72	    c#(a(x1)) -> c#(c(x1))
171.08/43.72	    c#(a(x1)) -> a#(c(c(x1)))
171.08/43.72	    c#(a(x1)) -> a#(a(c(c(x1))))
171.08/43.72	    c#(a(x1)) -> b#(a(a(c(c(x1)))))
171.08/43.72	   TRS:
171.08/43.72	    a(x1) -> b(x1)
171.08/43.72	    c(a(x1)) -> b(a(a(c(c(x1)))))
171.08/43.72	    b(b(x1)) -> x1
171.08/43.72	   TDG Processor:
171.08/43.72	    DPs:
171.08/43.72	     a#(x1) -> b#(x1)
171.08/43.72	     c#(a(x1)) -> c#(x1)
171.08/43.72	     c#(a(x1)) -> c#(c(x1))
171.08/43.72	     c#(a(x1)) -> a#(c(c(x1)))
171.08/43.72	     c#(a(x1)) -> a#(a(c(c(x1))))
171.08/43.72	     c#(a(x1)) -> b#(a(a(c(c(x1)))))
171.08/43.72	    TRS:
171.08/43.72	     a(x1) -> b(x1)
171.08/43.72	     c(a(x1)) -> b(a(a(c(c(x1)))))
171.08/43.72	     b(b(x1)) -> x1
171.08/43.72	    graph:
171.08/43.72	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(a(a(c(c(x1)))))
171.08/43.72	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(a(c(c(x1))))
171.08/43.72	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(c(c(x1)))
171.08/43.72	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
171.08/43.72	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1)
171.08/43.72	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(a(c(c(x1)))))
171.08/43.72	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(c(c(x1))))
171.08/43.72	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(c(x1)))
171.08/43.72	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1))
171.08/43.72	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
171.08/43.72	     c#(a(x1)) -> a#(c(c(x1))) -> a#(x1) -> b#(x1)
171.08/43.72	     c#(a(x1)) -> a#(a(c(c(x1)))) -> a#(x1) -> b#(x1)
171.08/43.72	    SCC Processor:
171.08/43.72	     #sccs: 1
171.08/43.72	     #rules: 2
171.08/43.72	     #arcs: 12/36
171.08/43.72	     DPs:
171.08/43.72	      c#(a(x1)) -> c#(c(x1))
171.08/43.72	      c#(a(x1)) -> c#(x1)
171.08/43.72	     TRS:
171.08/43.72	      a(x1) -> b(x1)
171.08/43.72	      c(a(x1)) -> b(a(a(c(c(x1)))))
171.08/43.72	      b(b(x1)) -> x1
171.08/43.72	     Arctic Interpretation Processor:
171.08/43.72	      dimension: 2
171.08/43.72	      usable rules:
171.08/43.72	       a(x1) -> b(x1)
171.08/43.72	       c(a(x1)) -> b(a(a(c(c(x1)))))
171.08/43.72	       b(b(x1)) -> x1
171.08/43.72	      interpretation:
171.08/43.72	       [c#](x0) = [2 1]x0 + [0],
171.08/43.72	       
171.08/43.72	                 [0  -&]  
171.08/43.72	       [c](x0) = [1  0 ]x0,
171.08/43.72	       
171.08/43.72	                 [-& 0 ]     [0]
171.08/43.72	       [b](x0) = [0  0 ]x0 + [1],
171.08/43.72	       
171.08/43.72	                 [1 0]     [2]
171.08/43.72	       [a](x0) = [0 0]x0 + [1]
171.08/43.72	      orientation:
171.08/43.72	       c#(a(x1)) = [3 2]x1 + [4] >= [2 1]x1 + [0] = c#(c(x1))
171.08/43.72	       
171.08/43.72	       c#(a(x1)) = [3 2]x1 + [4] >= [2 1]x1 + [0] = c#(x1)
171.08/43.72	       
171.08/43.72	               [1 0]     [2]    [-& 0 ]     [0]        
171.08/43.72	       a(x1) = [0 0]x1 + [1] >= [0  0 ]x1 + [1] = b(x1)
171.08/43.72	       
171.08/43.72	                  [1 0]     [2]    [1 0]     [2]                    
171.08/43.72	       c(a(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = b(a(a(c(c(x1)))))
171.08/43.72	       
171.08/43.72	                  [0 0]     [1]           
171.08/43.72	       b(b(x1)) = [0 0]x1 + [1] >= x1 = x1
171.08/43.72	      problem:
171.08/43.72	       DPs:
171.08/43.72	        
171.08/43.72	       TRS:
171.08/43.72	        a(x1) -> b(x1)
171.08/43.72	        c(a(x1)) -> b(a(a(c(c(x1)))))
171.08/43.72	        b(b(x1)) -> x1
171.08/43.72	      Qed
171.37/43.73	EOF