170.60/43.59	YES
170.60/43.59	
170.60/43.59	Problem:
170.60/43.59	 a(x1) -> x1
170.60/43.59	 a(b(x1)) -> b(a(c(b(a(x1)))))
170.60/43.59	 b(x1) -> x1
170.60/43.59	 c(c(c(x1))) -> x1
170.60/43.59	
170.60/43.59	Proof:
170.60/43.59	 String Reversal Processor:
170.60/43.59	  a(x1) -> x1
170.60/43.59	  b(a(x1)) -> a(b(c(a(b(x1)))))
170.60/43.59	  b(x1) -> x1
170.60/43.59	  c(c(c(x1))) -> x1
170.60/43.59	  DP Processor:
170.60/43.59	   DPs:
170.60/43.59	    b#(a(x1)) -> b#(x1)
170.60/43.59	    b#(a(x1)) -> a#(b(x1))
170.60/43.59	    b#(a(x1)) -> c#(a(b(x1)))
170.60/43.59	    b#(a(x1)) -> b#(c(a(b(x1))))
170.60/43.59	    b#(a(x1)) -> a#(b(c(a(b(x1)))))
170.60/43.59	   TRS:
170.60/43.59	    a(x1) -> x1
170.60/43.59	    b(a(x1)) -> a(b(c(a(b(x1)))))
170.60/43.59	    b(x1) -> x1
170.60/43.59	    c(c(c(x1))) -> x1
170.60/43.59	   TDG Processor:
170.60/43.59	    DPs:
170.60/43.59	     b#(a(x1)) -> b#(x1)
170.60/43.59	     b#(a(x1)) -> a#(b(x1))
170.60/43.59	     b#(a(x1)) -> c#(a(b(x1)))
170.60/43.59	     b#(a(x1)) -> b#(c(a(b(x1))))
170.60/43.59	     b#(a(x1)) -> a#(b(c(a(b(x1)))))
170.60/43.59	    TRS:
170.60/43.59	     a(x1) -> x1
170.60/43.59	     b(a(x1)) -> a(b(c(a(b(x1)))))
170.60/43.59	     b(x1) -> x1
170.60/43.59	     c(c(c(x1))) -> x1
170.60/43.59	    graph:
170.60/43.59	     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> a#(b(c(a(b(x1)))))
170.60/43.59	     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(c(a(b(x1))))
170.60/43.59	     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> c#(a(b(x1)))
170.60/43.59	     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> a#(b(x1))
170.60/43.59	     b#(a(x1)) -> b#(c(a(b(x1)))) -> b#(a(x1)) -> b#(x1)
170.60/43.59	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(c(a(b(x1)))))
170.60/43.59	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(c(a(b(x1))))
170.60/43.59	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(x1)))
170.60/43.59	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1))
170.60/43.59	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
170.60/43.59	    SCC Processor:
170.60/43.59	     #sccs: 1
170.60/43.59	     #rules: 2
170.60/43.59	     #arcs: 10/25
170.60/43.59	     DPs:
170.60/43.59	      b#(a(x1)) -> b#(c(a(b(x1))))
170.60/43.59	      b#(a(x1)) -> b#(x1)
170.60/43.59	     TRS:
170.60/43.59	      a(x1) -> x1
170.60/43.59	      b(a(x1)) -> a(b(c(a(b(x1)))))
170.60/43.59	      b(x1) -> x1
170.60/43.59	      c(c(c(x1))) -> x1
170.60/43.59	     Arctic Interpretation Processor:
170.60/43.59	      dimension: 2
170.60/43.59	      usable rules:
170.60/43.59	       a(x1) -> x1
170.60/43.59	       b(a(x1)) -> a(b(c(a(b(x1)))))
170.60/43.59	       b(x1) -> x1
170.60/43.59	       c(c(c(x1))) -> x1
170.60/43.59	      interpretation:
170.60/43.59	       [b#](x0) = [-& 2 ]x0 + [0],
170.60/43.59	       
170.60/43.59	                 [1  2 ]     [0 ]
170.60/43.59	       [c](x0) = [-3 -&]x0 + [-&],
170.60/43.59	       
170.60/43.59	                 [0  3 ]     [-&]
170.60/43.59	       [b](x0) = [-& 1 ]x0 + [0 ],
170.60/43.59	       
170.60/43.59	                 [0  -&]     [-&]
170.60/43.59	       [a](x0) = [-2 1 ]x0 + [1 ]
170.60/43.59	      orientation:
170.60/43.59	       b#(a(x1)) = [0 3]x1 + [3] >= [-1 2 ]x1 + [0] = b#(c(a(b(x1))))
170.60/43.59	       
170.60/43.59	       b#(a(x1)) = [0 3]x1 + [3] >= [-& 2 ]x1 + [0] = b#(x1)
170.60/43.59	       
170.60/43.59	               [0  -&]     [-&]           
170.60/43.59	       a(x1) = [-2 1 ]x1 + [1 ] >= x1 = x1
170.60/43.59	       
170.60/43.59	                  [1  4 ]     [4]    [1  4 ]     [3]                    
170.60/43.59	       b(a(x1)) = [-1 2 ]x1 + [2] >= [-1 2 ]x1 + [1] = a(b(c(a(b(x1)))))
170.60/43.59	       
170.60/43.59	               [0  3 ]     [-&]           
170.60/43.59	       b(x1) = [-& 1 ]x1 + [0 ] >= x1 = x1
170.60/43.59	       
170.60/43.59	                     [3  4 ]     [2 ]           
170.60/43.59	       c(c(c(x1))) = [-1 0 ]x1 + [-2] >= x1 = x1
170.60/43.59	      problem:
170.60/43.59	       DPs:
170.60/43.59	        
170.60/43.59	       TRS:
170.60/43.59	        a(x1) -> x1
170.60/43.59	        b(a(x1)) -> a(b(c(a(b(x1)))))
170.60/43.59	        b(x1) -> x1
170.60/43.59	        c(c(c(x1))) -> x1
170.60/43.59	      Qed
170.60/43.60	EOF