166.62/42.55	YES
166.62/42.56	
166.62/42.56	Problem:
166.62/42.56	 a(x1) -> x1
166.62/42.56	 a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	 b(b(x1)) -> b(x1)
166.62/42.56	
166.62/42.56	Proof:
166.62/42.56	 DP Processor:
166.62/42.56	  DPs:
166.62/42.56	   a#(a(b(x1))) -> a#(x1)
166.62/42.56	   a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	   a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	   a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	   a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	  TRS:
166.62/42.56	   a(x1) -> x1
166.62/42.56	   a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	   b(b(x1)) -> b(x1)
166.62/42.56	  TDG Processor:
166.62/42.56	   DPs:
166.62/42.56	    a#(a(b(x1))) -> a#(x1)
166.62/42.56	    a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	    a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	   TRS:
166.62/42.56	    a(x1) -> x1
166.62/42.56	    a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	    b(b(x1)) -> b(x1)
166.62/42.56	   graph:
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
166.62/42.56	    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
166.62/42.56	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
166.62/42.56	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
166.62/42.56	   EDG Processor:
166.62/42.56	    DPs:
166.62/42.56	     a#(a(b(x1))) -> a#(x1)
166.62/42.56	     a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	     a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	     a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	     a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	    TRS:
166.62/42.56	     a(x1) -> x1
166.62/42.56	     a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	     b(b(x1)) -> b(x1)
166.62/42.56	    graph:
166.62/42.56	     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
166.62/42.56	     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
166.62/42.56	     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
166.62/42.56	     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
166.62/42.56	     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
166.62/42.56	    SCC Processor:
166.62/42.56	     #sccs: 1
166.62/42.56	     #rules: 2
166.62/42.56	     #arcs: 10/25
166.62/42.56	     DPs:
166.62/42.56	      a#(a(b(x1))) -> a#(a(x1))
166.62/42.56	      a#(a(b(x1))) -> a#(x1)
166.62/42.56	     TRS:
166.62/42.56	      a(x1) -> x1
166.62/42.56	      a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	      b(b(x1)) -> b(x1)
166.62/42.56	     Bounds Processor:
166.62/42.56	      bound: 0
166.62/42.56	      enrichment: match-dp
166.62/42.56	      automaton:
166.62/42.56	       final states: {1}
166.62/42.56	       transitions:
166.62/42.56	        a{#,0}(3) -> 1*
166.62/42.56	        a0(2) -> 3*
166.62/42.56	        a0(9) -> 10*
166.62/42.56	        a0(11) -> 12*
166.62/42.56	        b0(10) -> 11*
166.62/42.56	        b0(12) -> 13*
166.62/42.56	        f40() -> 2*
166.62/42.56	        2 -> 3*
166.62/42.56	        3 -> 9*
166.62/42.56	        9 -> 10*
166.62/42.56	        11 -> 13,3,10,12
166.62/42.56	        13 -> 11,12,3
166.62/42.56	      problem:
166.62/42.56	       DPs:
166.62/42.56	        a#(a(b(x1))) -> a#(x1)
166.62/42.56	       TRS:
166.62/42.56	        a(x1) -> x1
166.62/42.56	        a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	        b(b(x1)) -> b(x1)
166.62/42.56	      Restore Modifier:
166.62/42.56	       DPs:
166.62/42.56	        a#(a(b(x1))) -> a#(x1)
166.62/42.56	       TRS:
166.62/42.56	        a(x1) -> x1
166.62/42.56	        a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	        b(b(x1)) -> b(x1)
166.62/42.56	       EDG Processor:
166.62/42.56	        DPs:
166.62/42.56	         a#(a(b(x1))) -> a#(x1)
166.62/42.56	        TRS:
166.62/42.56	         a(x1) -> x1
166.62/42.56	         a(a(b(x1))) -> b(a(b(a(a(x1)))))
166.62/42.56	         b(b(x1)) -> b(x1)
166.62/42.56	        graph:
166.62/42.56	         a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
166.62/42.56	        Usable Rule Processor:
166.62/42.56	         DPs:
166.62/42.56	          a#(a(b(x1))) -> a#(x1)
166.62/42.56	         TRS:
166.62/42.56	          
166.62/42.56	         Arctic Interpretation Processor:
166.62/42.56	          dimension: 1
166.62/42.56	          usable rules:
166.62/42.56	           
166.62/42.56	          interpretation:
166.62/42.56	           [a#](x0) = 6x0,
166.62/42.56	           
166.62/42.56	           [b](x0) = x0 + 9,
166.62/42.56	           
166.62/42.56	           [a](x0) = 1x0 + 12
166.62/42.56	          orientation:
166.62/42.56	           a#(a(b(x1))) = 7x1 + 18 >= 6x1 = a#(x1)
166.62/42.56	          problem:
166.62/42.56	           DPs:
166.62/42.56	            
166.62/42.56	           TRS:
166.62/42.56	            
166.62/42.56	          Qed
166.62/42.56	EOF