165.77/42.28	YES
165.77/42.29	
165.77/42.29	Problem:
165.77/42.29	 a(x1) -> x1
165.77/42.29	 a(b(x1)) -> b(b(a(c(x1))))
165.77/42.29	 b(x1) -> x1
165.77/42.29	 c(c(x1)) -> a(x1)
165.77/42.29	
165.77/42.29	Proof:
165.77/42.29	 String Reversal Processor:
165.77/42.29	  a(x1) -> x1
165.77/42.29	  b(a(x1)) -> c(a(b(b(x1))))
165.77/42.29	  b(x1) -> x1
165.77/42.29	  c(c(x1)) -> a(x1)
165.77/42.29	  DP Processor:
165.77/42.29	   DPs:
165.77/42.29	    b#(a(x1)) -> b#(x1)
165.77/42.29	    b#(a(x1)) -> b#(b(x1))
165.77/42.29	    b#(a(x1)) -> a#(b(b(x1)))
165.77/42.29	    b#(a(x1)) -> c#(a(b(b(x1))))
165.77/42.29	    c#(c(x1)) -> a#(x1)
165.77/42.29	   TRS:
165.77/42.29	    a(x1) -> x1
165.77/42.29	    b(a(x1)) -> c(a(b(b(x1))))
165.77/42.29	    b(x1) -> x1
165.77/42.29	    c(c(x1)) -> a(x1)
165.77/42.29	   TDG Processor:
165.77/42.29	    DPs:
165.77/42.29	     b#(a(x1)) -> b#(x1)
165.77/42.29	     b#(a(x1)) -> b#(b(x1))
165.77/42.29	     b#(a(x1)) -> a#(b(b(x1)))
165.77/42.29	     b#(a(x1)) -> c#(a(b(b(x1))))
165.77/42.29	     c#(c(x1)) -> a#(x1)
165.77/42.29	    TRS:
165.77/42.29	     a(x1) -> x1
165.77/42.29	     b(a(x1)) -> c(a(b(b(x1))))
165.77/42.29	     b(x1) -> x1
165.77/42.29	     c(c(x1)) -> a(x1)
165.77/42.29	    graph:
165.77/42.29	     b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(c(x1)) -> a#(x1)
165.77/42.29	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(b(x1))))
165.77/42.29	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
165.77/42.29	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
165.77/42.29	     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
165.77/42.29	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
165.77/42.29	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
165.77/42.29	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
165.77/42.29	     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
165.77/42.29	    SCC Processor:
165.77/42.29	     #sccs: 1
165.77/42.29	     #rules: 2
165.77/42.29	     #arcs: 9/25
165.77/42.29	     DPs:
165.77/42.29	      b#(a(x1)) -> b#(b(x1))
165.77/42.29	      b#(a(x1)) -> b#(x1)
165.77/42.29	     TRS:
165.77/42.29	      a(x1) -> x1
165.77/42.29	      b(a(x1)) -> c(a(b(b(x1))))
165.77/42.29	      b(x1) -> x1
165.77/42.29	      c(c(x1)) -> a(x1)
165.77/42.29	     Arctic Interpretation Processor:
165.77/42.29	      dimension: 2
165.77/42.29	      usable rules:
165.77/42.29	       a(x1) -> x1
165.77/42.29	       b(a(x1)) -> c(a(b(b(x1))))
165.77/42.29	       b(x1) -> x1
165.77/42.29	       c(c(x1)) -> a(x1)
165.77/42.29	      interpretation:
165.77/42.29	       [b#](x0) = [0 0]x0,
165.77/42.29	       
165.77/42.29	                 [-& 1 ]     [0]
165.77/42.29	       [c](x0) = [0  0 ]x0 + [1],
165.77/42.29	       
165.77/42.29	                 [0 0]     [0]
165.77/42.29	       [b](x0) = [0 0]x0 + [1],
165.77/42.29	       
165.77/42.29	                 [1 1]     [2]
165.77/42.29	       [a](x0) = [0 0]x0 + [0]
165.77/42.29	      orientation:
165.77/42.29	       b#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 + [1] = b#(b(x1))
165.77/42.29	       
165.77/42.29	       b#(a(x1)) = [1 1]x1 + [2] >= [0 0]x1 = b#(x1)
165.77/42.29	       
165.77/42.29	               [1 1]     [2]           
165.77/42.29	       a(x1) = [0 0]x1 + [0] >= x1 = x1
165.77/42.29	       
165.77/42.29	                  [1 1]     [2]    [1 1]     [2]                 
165.77/42.29	       b(a(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = c(a(b(b(x1))))
165.77/42.29	       
165.77/42.29	               [0 0]     [0]           
165.77/42.29	       b(x1) = [0 0]x1 + [1] >= x1 = x1
165.77/42.29	       
165.77/42.29	                  [1 1]     [2]    [1 1]     [2]        
165.77/42.29	       c(c(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [0] = a(x1)
165.77/42.29	      problem:
165.77/42.29	       DPs:
165.77/42.29	        
165.77/42.29	       TRS:
165.77/42.29	        a(x1) -> x1
165.77/42.29	        b(a(x1)) -> c(a(b(b(x1))))
165.77/42.29	        b(x1) -> x1
165.77/42.29	        c(c(x1)) -> a(x1)
165.77/42.29	      Qed
165.85/42.29	EOF