167.72/42.97	YES
167.72/42.98	
167.72/42.98	Problem:
167.72/42.98	 a(x1) -> x1
167.72/42.98	 a(x1) -> b(x1)
167.72/42.98	 b(x1) -> x1
167.72/42.98	 b(a(c(x1))) -> c(c(b(a(a(x1)))))
167.72/42.98	
167.72/42.98	Proof:
167.72/42.98	 String Reversal Processor:
167.72/42.98	  a(x1) -> x1
167.72/42.98	  a(x1) -> b(x1)
167.72/42.98	  b(x1) -> x1
167.72/42.98	  c(a(b(x1))) -> a(a(b(c(c(x1)))))
167.72/42.98	  DP Processor:
167.72/42.98	   DPs:
167.72/42.98	    a#(x1) -> b#(x1)
167.72/42.98	    c#(a(b(x1))) -> c#(x1)
167.72/42.98	    c#(a(b(x1))) -> c#(c(x1))
167.72/42.98	    c#(a(b(x1))) -> b#(c(c(x1)))
167.72/42.98	    c#(a(b(x1))) -> a#(b(c(c(x1))))
167.72/42.98	    c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
167.72/42.98	   TRS:
167.72/42.98	    a(x1) -> x1
167.72/42.98	    a(x1) -> b(x1)
167.72/42.98	    b(x1) -> x1
167.72/42.98	    c(a(b(x1))) -> a(a(b(c(c(x1)))))
167.72/42.98	   TDG Processor:
167.72/42.98	    DPs:
167.72/42.98	     a#(x1) -> b#(x1)
167.72/42.98	     c#(a(b(x1))) -> c#(x1)
167.72/42.98	     c#(a(b(x1))) -> c#(c(x1))
167.72/42.98	     c#(a(b(x1))) -> b#(c(c(x1)))
167.72/42.98	     c#(a(b(x1))) -> a#(b(c(c(x1))))
167.72/42.98	     c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
167.72/42.98	    TRS:
167.72/42.98	     a(x1) -> x1
167.72/42.98	     a(x1) -> b(x1)
167.72/42.98	     b(x1) -> x1
167.72/42.98	     c(a(b(x1))) -> a(a(b(c(c(x1)))))
167.72/42.98	    graph:
167.72/42.98	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
167.72/42.98	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> a#(b(c(c(x1))))
167.72/42.98	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> b#(c(c(x1)))
167.72/42.98	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(c(x1))
167.72/42.98	     c#(a(b(x1))) -> c#(c(x1)) -> c#(a(b(x1))) -> c#(x1)
167.72/42.98	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(a(b(c(c(x1)))))
167.72/42.98	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> a#(b(c(c(x1))))
167.72/42.98	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> b#(c(c(x1)))
167.72/42.98	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(c(x1))
167.72/42.98	     c#(a(b(x1))) -> c#(x1) -> c#(a(b(x1))) -> c#(x1)
167.72/42.98	     c#(a(b(x1))) -> a#(b(c(c(x1)))) -> a#(x1) -> b#(x1)
167.72/42.98	     c#(a(b(x1))) -> a#(a(b(c(c(x1))))) -> a#(x1) -> b#(x1)
167.72/42.98	    SCC Processor:
167.72/42.98	     #sccs: 1
167.72/42.98	     #rules: 2
167.72/42.98	     #arcs: 12/36
167.72/42.98	     DPs:
167.72/42.98	      c#(a(b(x1))) -> c#(c(x1))
167.72/42.98	      c#(a(b(x1))) -> c#(x1)
167.72/42.98	     TRS:
167.72/42.98	      a(x1) -> x1
167.72/42.98	      a(x1) -> b(x1)
167.72/42.98	      b(x1) -> x1
167.72/42.98	      c(a(b(x1))) -> a(a(b(c(c(x1)))))
167.72/42.98	     Arctic Interpretation Processor:
167.72/42.98	      dimension: 2
167.72/42.98	      usable rules:
167.72/42.98	       a(x1) -> x1
167.72/42.98	       a(x1) -> b(x1)
167.72/42.98	       b(x1) -> x1
167.72/42.98	       c(a(b(x1))) -> a(a(b(c(c(x1)))))
167.72/42.98	      interpretation:
167.72/42.98	       [c#](x0) = [0 2]x0 + [0],
167.72/42.98	       
167.72/42.98	                 [0  0 ]     [0 ]
167.72/42.98	       [c](x0) = [-& 0 ]x0 + [-&],
167.72/42.98	       
167.72/42.98	                 [0 0]     [2]
167.72/42.98	       [b](x0) = [0 0]x0 + [0],
167.72/42.98	       
167.72/42.98	                 [0 0]     [2]
167.72/42.98	       [a](x0) = [2 0]x0 + [0]
167.72/42.98	      orientation:
167.72/42.98	       c#(a(b(x1))) = [4 4]x1 + [6] >= [0 2]x1 + [0] = c#(c(x1))
167.72/42.98	       
167.72/42.98	       c#(a(b(x1))) = [4 4]x1 + [6] >= [0 2]x1 + [0] = c#(x1)
167.72/42.98	       
167.72/42.98	               [0 0]     [2]           
167.72/42.98	       a(x1) = [2 0]x1 + [0] >= x1 = x1
167.72/42.98	       
167.72/42.98	               [0 0]     [2]    [0 0]     [2]        
167.72/42.98	       a(x1) = [2 0]x1 + [0] >= [0 0]x1 + [0] = b(x1)
167.72/42.98	       
167.72/42.98	               [0 0]     [2]           
167.72/42.98	       b(x1) = [0 0]x1 + [0] >= x1 = x1
167.72/42.98	       
167.72/42.98	                     [2 2]     [4]    [2 2]     [4]                    
167.72/42.98	       c(a(b(x1))) = [2 2]x1 + [4] >= [2 2]x1 + [4] = a(a(b(c(c(x1)))))
167.72/42.98	      problem:
167.72/42.98	       DPs:
167.72/42.98	        
167.72/42.98	       TRS:
167.72/42.98	        a(x1) -> x1
167.72/42.98	        a(x1) -> b(x1)
167.72/42.98	        b(x1) -> x1
167.72/42.98	        c(a(b(x1))) -> a(a(b(c(c(x1)))))
167.72/42.98	      Qed
167.72/42.98	EOF