168.13/44.54	YES
168.13/44.55	
168.13/44.55	Problem:
168.13/44.55	 a(x1) -> b(x1)
168.13/44.55	 a(c(x1)) -> c(c(c(a(a(b(x1))))))
168.13/44.55	 b(b(x1)) -> x1
168.13/44.55	
168.13/44.55	Proof:
168.13/44.55	 String Reversal Processor:
168.13/44.55	  a(x1) -> b(x1)
168.13/44.55	  c(a(x1)) -> b(a(a(c(c(c(x1))))))
168.13/44.55	  b(b(x1)) -> x1
168.13/44.55	  DP Processor:
168.13/44.55	   DPs:
168.13/44.55	    a#(x1) -> b#(x1)
168.13/44.55	    c#(a(x1)) -> c#(x1)
168.13/44.55	    c#(a(x1)) -> c#(c(x1))
168.13/44.55	    c#(a(x1)) -> c#(c(c(x1)))
168.13/44.55	    c#(a(x1)) -> a#(c(c(c(x1))))
168.13/44.55	    c#(a(x1)) -> a#(a(c(c(c(x1)))))
168.13/44.55	    c#(a(x1)) -> b#(a(a(c(c(c(x1))))))
168.13/44.55	   TRS:
168.13/44.55	    a(x1) -> b(x1)
168.13/44.55	    c(a(x1)) -> b(a(a(c(c(c(x1))))))
168.13/44.55	    b(b(x1)) -> x1
168.13/44.55	   TDG Processor:
168.13/44.55	    DPs:
168.13/44.55	     a#(x1) -> b#(x1)
168.13/44.55	     c#(a(x1)) -> c#(x1)
168.13/44.55	     c#(a(x1)) -> c#(c(x1))
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1)))
168.13/44.55	     c#(a(x1)) -> a#(c(c(c(x1))))
168.13/44.55	     c#(a(x1)) -> a#(a(c(c(c(x1)))))
168.13/44.55	     c#(a(x1)) -> b#(a(a(c(c(c(x1))))))
168.13/44.55	    TRS:
168.13/44.55	     a(x1) -> b(x1)
168.13/44.55	     c(a(x1)) -> b(a(a(c(c(c(x1))))))
168.13/44.55	     b(b(x1)) -> x1
168.13/44.55	    graph:
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1))) -> c#(a(x1)) -> b#(a(a(c(c(c(x1))))))
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1))) -> c#(a(x1)) -> a#(a(c(c(c(x1)))))
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1))) -> c#(a(x1)) -> a#(c(c(c(x1))))
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1))) -> c#(a(x1)) -> c#(c(c(x1)))
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1))) -> c#(a(x1)) -> c#(c(x1))
168.13/44.55	     c#(a(x1)) -> c#(c(c(x1))) -> c#(a(x1)) -> c#(x1)
168.13/44.55	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(a(a(c(c(c(x1))))))
168.13/44.55	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(a(c(c(c(x1)))))
168.13/44.55	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(c(c(c(x1))))
168.13/44.55	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(c(x1)))
168.13/44.55	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
168.13/44.55	     c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1)
168.13/44.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(a(a(c(c(c(x1))))))
168.13/44.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(a(c(c(c(x1)))))
168.13/44.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(c(c(x1))))
168.13/44.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(c(x1)))
168.13/44.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1))
168.13/44.55	     c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
168.13/44.55	     c#(a(x1)) -> a#(c(c(c(x1)))) -> a#(x1) -> b#(x1)
168.13/44.55	     c#(a(x1)) -> a#(a(c(c(c(x1))))) -> a#(x1) -> b#(x1)
168.13/44.55	    SCC Processor:
168.13/44.55	     #sccs: 1
168.13/44.55	     #rules: 3
168.13/44.55	     #arcs: 20/49
168.13/44.55	     DPs:
168.13/44.55	      c#(a(x1)) -> c#(c(c(x1)))
168.13/44.55	      c#(a(x1)) -> c#(x1)
168.13/44.55	      c#(a(x1)) -> c#(c(x1))
168.13/44.55	     TRS:
168.13/44.55	      a(x1) -> b(x1)
168.13/44.55	      c(a(x1)) -> b(a(a(c(c(c(x1))))))
168.13/44.55	      b(b(x1)) -> x1
168.13/44.55	     Arctic Interpretation Processor:
168.13/44.55	      dimension: 2
168.13/44.55	      usable rules:
168.13/44.55	       a(x1) -> b(x1)
168.13/44.55	       c(a(x1)) -> b(a(a(c(c(c(x1))))))
168.13/44.55	       b(b(x1)) -> x1
168.13/44.55	      interpretation:
168.13/44.55	       [c#](x0) = [0 2]x0 + [0],
168.13/44.55	       
168.13/44.55	                 [0  1 ]     [2]
168.13/44.55	       [c](x0) = [-& 0 ]x0 + [0],
168.13/44.55	       
168.13/44.55	                 [0  0 ]     [0 ]
168.13/44.55	       [b](x0) = [0  -&]x0 + [-&],
168.13/44.55	       
168.13/44.55	                 [0 0]     [0]
168.13/44.55	       [a](x0) = [0 1]x0 + [2]
168.13/44.55	      orientation:
168.13/44.55	       c#(a(x1)) = [2 3]x1 + [4] >= [0 2]x1 + [2] = c#(c(c(x1)))
168.13/44.55	       
168.13/44.55	       c#(a(x1)) = [2 3]x1 + [4] >= [0 2]x1 + [0] = c#(x1)
168.13/44.55	       
168.13/44.55	       c#(a(x1)) = [2 3]x1 + [4] >= [0 2]x1 + [2] = c#(c(x1))
168.13/44.55	       
168.13/44.55	               [0 0]     [0]    [0  0 ]     [0 ]        
168.13/44.55	       a(x1) = [0 1]x1 + [2] >= [0  -&]x1 + [-&] = b(x1)
168.13/44.55	       
168.13/44.55	                  [1 2]     [3]    [1 2]     [3]                       
168.13/44.55	       c(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = b(a(a(c(c(c(x1))))))
168.13/44.55	       
168.13/44.55	                  [0 0]     [0]           
168.13/44.55	       b(b(x1)) = [0 0]x1 + [0] >= x1 = x1
168.13/44.55	      problem:
168.13/44.55	       DPs:
168.13/44.55	        
168.13/44.55	       TRS:
168.13/44.55	        a(x1) -> b(x1)
168.13/44.55	        c(a(x1)) -> b(a(a(c(c(c(x1))))))
168.13/44.55	        b(b(x1)) -> x1
168.13/44.55	      Qed
168.13/44.55	EOF