166.59/42.53	YES
166.59/42.53	
166.59/42.53	Problem:
166.59/42.53	 a(x1) -> b(x1)
166.59/42.53	 a(b(x1)) -> x1
166.59/42.53	 b(a(x1)) -> a(c(a(b(x1))))
166.59/42.53	 c(c(x1)) -> x1
166.59/42.53	
166.59/42.53	Proof:
166.59/42.53	 String Reversal Processor:
166.59/42.53	  a(x1) -> b(x1)
166.59/42.53	  b(a(x1)) -> x1
166.59/42.53	  a(b(x1)) -> b(a(c(a(x1))))
166.59/42.53	  c(c(x1)) -> x1
166.59/42.53	  DP Processor:
166.59/42.53	   DPs:
166.59/42.53	    a#(x1) -> b#(x1)
166.59/42.53	    a#(b(x1)) -> a#(x1)
166.59/42.53	    a#(b(x1)) -> c#(a(x1))
166.59/42.53	    a#(b(x1)) -> a#(c(a(x1)))
166.59/42.53	    a#(b(x1)) -> b#(a(c(a(x1))))
166.59/42.53	   TRS:
166.59/42.53	    a(x1) -> b(x1)
166.59/42.53	    b(a(x1)) -> x1
166.59/42.53	    a(b(x1)) -> b(a(c(a(x1))))
166.59/42.53	    c(c(x1)) -> x1
166.59/42.53	   TDG Processor:
166.59/42.53	    DPs:
166.59/42.53	     a#(x1) -> b#(x1)
166.59/42.53	     a#(b(x1)) -> a#(x1)
166.59/42.53	     a#(b(x1)) -> c#(a(x1))
166.59/42.53	     a#(b(x1)) -> a#(c(a(x1)))
166.59/42.53	     a#(b(x1)) -> b#(a(c(a(x1))))
166.59/42.53	    TRS:
166.59/42.53	     a(x1) -> b(x1)
166.59/42.53	     b(a(x1)) -> x1
166.59/42.53	     a(b(x1)) -> b(a(c(a(x1))))
166.59/42.53	     c(c(x1)) -> x1
166.59/42.53	    graph:
166.59/42.53	     a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> b#(a(c(a(x1))))
166.59/42.53	     a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(c(a(x1)))
166.59/42.53	     a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> c#(a(x1))
166.59/42.53	     a#(b(x1)) -> a#(c(a(x1))) -> a#(b(x1)) -> a#(x1)
166.59/42.53	     a#(b(x1)) -> a#(c(a(x1))) -> a#(x1) -> b#(x1)
166.59/42.53	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(c(a(x1))))
166.59/42.53	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(a(x1)))
166.59/42.53	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
166.59/42.53	     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
166.59/42.53	     a#(b(x1)) -> a#(x1) -> a#(x1) -> b#(x1)
166.59/42.53	    SCC Processor:
166.59/42.53	     #sccs: 1
166.59/42.53	     #rules: 2
166.59/42.53	     #arcs: 10/25
166.59/42.53	     DPs:
166.59/42.53	      a#(b(x1)) -> a#(c(a(x1)))
166.59/42.53	      a#(b(x1)) -> a#(x1)
166.59/42.53	     TRS:
166.59/42.53	      a(x1) -> b(x1)
166.59/42.53	      b(a(x1)) -> x1
166.59/42.53	      a(b(x1)) -> b(a(c(a(x1))))
166.59/42.53	      c(c(x1)) -> x1
166.59/42.53	     Arctic Interpretation Processor:
166.59/42.53	      dimension: 2
166.59/42.53	      usable rules:
166.59/42.53	       a(x1) -> b(x1)
166.59/42.53	       b(a(x1)) -> x1
166.59/42.53	       a(b(x1)) -> b(a(c(a(x1))))
166.59/42.53	       c(c(x1)) -> x1
166.59/42.53	      interpretation:
166.59/42.53	       [a#](x0) = [1 2]x0,
166.59/42.53	       
166.59/42.53	                 [0  0 ]     [0]
166.59/42.53	       [c](x0) = [0  -&]x0 + [0],
166.59/42.53	       
166.59/42.53	                 [-& 0 ]     [0]
166.59/42.53	       [b](x0) = [0  2 ]x0 + [3],
166.59/42.53	       
166.59/42.53	                 [-& 0 ]     [0]
166.59/42.53	       [a](x0) = [0  2 ]x0 + [3]
166.59/42.53	      orientation:
166.59/42.53	       a#(b(x1)) = [2 4]x1 + [5] >= [1 3]x1 + [4] = a#(c(a(x1)))
166.59/42.53	       
166.59/42.53	       a#(b(x1)) = [2 4]x1 + [5] >= [1 2]x1 = a#(x1)
166.59/42.53	       
166.59/42.53	               [-& 0 ]     [0]    [-& 0 ]     [0]        
166.59/42.53	       a(x1) = [0  2 ]x1 + [3] >= [0  2 ]x1 + [3] = b(x1)
166.59/42.53	       
166.59/42.53	                  [0 2]     [3]           
166.59/42.53	       b(a(x1)) = [2 4]x1 + [5] >= x1 = x1
166.59/42.53	       
166.59/42.53	                  [0 2]     [3]    [0 2]     [3]                 
166.59/42.53	       a(b(x1)) = [2 4]x1 + [5] >= [2 4]x1 + [5] = b(a(c(a(x1))))
166.59/42.53	       
166.59/42.53	                  [0 0]     [0]           
166.59/42.53	       c(c(x1)) = [0 0]x1 + [0] >= x1 = x1
166.59/42.53	      problem:
166.59/42.53	       DPs:
166.59/42.53	        
166.59/42.53	       TRS:
166.59/42.53	        a(x1) -> b(x1)
166.59/42.53	        b(a(x1)) -> x1
166.59/42.53	        a(b(x1)) -> b(a(c(a(x1))))
166.59/42.53	        c(c(x1)) -> x1
166.59/42.53	      Qed
166.59/42.54	EOF