168.71/43.13	YES
168.71/43.13	
168.71/43.13	Problem:
168.71/43.13	 a(x1) -> x1
168.71/43.13	 a(x1) -> b(x1)
168.71/43.13	 a(b(c(x1))) -> c(c(a(b(a(x1)))))
168.71/43.13	 c(x1) -> x1
168.71/43.13	
168.71/43.13	Proof:
168.71/43.13	 String Reversal Processor:
168.71/43.13	  a(x1) -> x1
168.71/43.13	  a(x1) -> b(x1)
168.71/43.13	  c(b(a(x1))) -> a(b(a(c(c(x1)))))
168.71/43.13	  c(x1) -> x1
168.71/43.13	  DP Processor:
168.71/43.13	   DPs:
168.71/43.13	    c#(b(a(x1))) -> c#(x1)
168.71/43.13	    c#(b(a(x1))) -> c#(c(x1))
168.71/43.13	    c#(b(a(x1))) -> a#(c(c(x1)))
168.71/43.13	    c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
168.71/43.13	   TRS:
168.71/43.13	    a(x1) -> x1
168.71/43.13	    a(x1) -> b(x1)
168.71/43.13	    c(b(a(x1))) -> a(b(a(c(c(x1)))))
168.71/43.13	    c(x1) -> x1
168.71/43.13	   TDG Processor:
168.71/43.13	    DPs:
168.71/43.13	     c#(b(a(x1))) -> c#(x1)
168.71/43.13	     c#(b(a(x1))) -> c#(c(x1))
168.71/43.13	     c#(b(a(x1))) -> a#(c(c(x1)))
168.71/43.13	     c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
168.71/43.13	    TRS:
168.71/43.13	     a(x1) -> x1
168.71/43.13	     a(x1) -> b(x1)
168.71/43.13	     c(b(a(x1))) -> a(b(a(c(c(x1)))))
168.71/43.13	     c(x1) -> x1
168.71/43.13	    graph:
168.71/43.13	     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
168.71/43.13	     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> a#(c(c(x1)))
168.71/43.13	     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(c(x1))
168.71/43.13	     c#(b(a(x1))) -> c#(c(x1)) -> c#(b(a(x1))) -> c#(x1)
168.71/43.13	     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(b(a(c(c(x1)))))
168.71/43.13	     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> a#(c(c(x1)))
168.71/43.13	     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(c(x1))
168.71/43.13	     c#(b(a(x1))) -> c#(x1) -> c#(b(a(x1))) -> c#(x1)
168.71/43.13	    SCC Processor:
168.71/43.13	     #sccs: 1
168.71/43.13	     #rules: 2
168.71/43.13	     #arcs: 8/16
168.71/43.13	     DPs:
168.71/43.13	      c#(b(a(x1))) -> c#(c(x1))
168.71/43.13	      c#(b(a(x1))) -> c#(x1)
168.71/43.13	     TRS:
168.71/43.13	      a(x1) -> x1
168.71/43.13	      a(x1) -> b(x1)
168.71/43.13	      c(b(a(x1))) -> a(b(a(c(c(x1)))))
168.71/43.13	      c(x1) -> x1
168.71/43.13	     Arctic Interpretation Processor:
168.71/43.13	      dimension: 2
168.71/43.13	      usable rules:
168.71/43.13	       a(x1) -> x1
168.71/43.13	       a(x1) -> b(x1)
168.71/43.13	       c(b(a(x1))) -> a(b(a(c(c(x1)))))
168.71/43.13	       c(x1) -> x1
168.71/43.13	      interpretation:
168.71/43.13	       [c#](x0) = [0 3]x0,
168.71/43.13	       
168.71/43.13	                 [0 0]     [0]
168.71/43.13	       [c](x0) = [0 0]x0 + [2],
168.71/43.13	       
168.71/43.13	                 [0  -&]     [-&]
168.71/43.13	       [b](x0) = [1  0 ]x0 + [0 ],
168.71/43.13	       
168.71/43.13	                 [0 0]     [-&]
168.71/43.13	       [a](x0) = [1 0]x0 + [3 ]
168.71/43.13	      orientation:
168.71/43.13	       c#(b(a(x1))) = [4 4]x1 + [6] >= [3 3]x1 + [5] = c#(c(x1))
168.71/43.13	       
168.71/43.13	       c#(b(a(x1))) = [4 4]x1 + [6] >= [0 3]x1 = c#(x1)
168.71/43.13	       
168.71/43.13	               [0 0]     [-&]           
168.71/43.13	       a(x1) = [1 0]x1 + [3 ] >= x1 = x1
168.71/43.13	       
168.71/43.13	               [0 0]     [-&]    [0  -&]     [-&]        
168.71/43.13	       a(x1) = [1 0]x1 + [3 ] >= [1  0 ]x1 + [0 ] = b(x1)
168.71/43.13	       
168.71/43.13	                     [1 1]     [3]    [1 1]     [3]                    
168.71/43.13	       c(b(a(x1))) = [1 1]x1 + [3] >= [1 1]x1 + [3] = a(b(a(c(c(x1)))))
168.71/43.13	       
168.71/43.13	               [0 0]     [0]           
168.71/43.13	       c(x1) = [0 0]x1 + [2] >= x1 = x1
168.71/43.13	      problem:
168.71/43.13	       DPs:
168.71/43.13	        
168.71/43.13	       TRS:
168.71/43.13	        a(x1) -> x1
168.71/43.13	        a(x1) -> b(x1)
168.71/43.13	        c(b(a(x1))) -> a(b(a(c(c(x1)))))
168.71/43.13	        c(x1) -> x1
168.71/43.13	      Qed
168.87/43.14	EOF