166.90/42.60	YES
166.90/42.60	
166.90/42.60	Problem:
166.90/42.60	 a(x1) -> b(c(x1))
166.90/42.60	 a(b(b(x1))) -> b(b(a(a(x1))))
166.90/42.60	 b(a(x1)) -> x1
166.90/42.60	
166.90/42.60	Proof:
166.90/42.60	 DP Processor:
166.90/42.60	  DPs:
166.90/42.60	   a#(x1) -> b#(c(x1))
166.90/42.60	   a#(b(b(x1))) -> a#(x1)
166.90/42.60	   a#(b(b(x1))) -> a#(a(x1))
166.90/42.60	   a#(b(b(x1))) -> b#(a(a(x1)))
166.90/42.60	   a#(b(b(x1))) -> b#(b(a(a(x1))))
166.90/42.60	  TRS:
166.90/42.60	   a(x1) -> b(c(x1))
166.90/42.60	   a(b(b(x1))) -> b(b(a(a(x1))))
166.90/42.60	   b(a(x1)) -> x1
166.90/42.60	  TDG Processor:
166.90/42.60	   DPs:
166.90/42.60	    a#(x1) -> b#(c(x1))
166.90/42.60	    a#(b(b(x1))) -> a#(x1)
166.90/42.60	    a#(b(b(x1))) -> a#(a(x1))
166.90/42.60	    a#(b(b(x1))) -> b#(a(a(x1)))
166.90/42.60	    a#(b(b(x1))) -> b#(b(a(a(x1))))
166.90/42.60	   TRS:
166.90/42.60	    a(x1) -> b(c(x1))
166.90/42.60	    a(b(b(x1))) -> b(b(a(a(x1))))
166.90/42.60	    b(a(x1)) -> x1
166.90/42.60	   graph:
166.90/42.60	    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> b#(b(a(a(x1))))
166.90/42.60	    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> b#(a(a(x1)))
166.90/42.60	    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(a(x1))
166.90/42.60	    a#(b(b(x1))) -> a#(a(x1)) -> a#(b(b(x1))) -> a#(x1)
166.90/42.60	    a#(b(b(x1))) -> a#(a(x1)) -> a#(x1) -> b#(c(x1))
166.90/42.60	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(b(a(a(x1))))
166.90/42.60	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(a(a(x1)))
166.90/42.60	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(a(x1))
166.90/42.60	    a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
166.90/42.60	    a#(b(b(x1))) -> a#(x1) -> a#(x1) -> b#(c(x1))
166.90/42.60	   SCC Processor:
166.90/42.60	    #sccs: 1
166.90/42.60	    #rules: 2
166.90/42.60	    #arcs: 10/25
166.90/42.60	    DPs:
166.90/42.60	     a#(b(b(x1))) -> a#(a(x1))
166.90/42.60	     a#(b(b(x1))) -> a#(x1)
166.90/42.60	    TRS:
166.90/42.60	     a(x1) -> b(c(x1))
166.90/42.60	     a(b(b(x1))) -> b(b(a(a(x1))))
166.90/42.60	     b(a(x1)) -> x1
166.90/42.60	    Arctic Interpretation Processor:
166.90/42.60	     dimension: 2
166.90/42.60	     usable rules:
166.90/42.60	      a(x1) -> b(c(x1))
166.90/42.60	      a(b(b(x1))) -> b(b(a(a(x1))))
166.90/42.60	      b(a(x1)) -> x1
166.90/42.60	     interpretation:
166.90/42.60	      [a#](x0) = [0 0]x0 + [0],
166.90/42.60	      
166.90/42.60	                [-& 1 ]     [0]
166.90/42.60	      [b](x0) = [0  -&]x0 + [2],
166.90/42.60	      
166.90/42.60	                [0  0 ]     [2]
166.90/42.60	      [c](x0) = [-& -&]x0 + [0],
166.90/42.60	      
166.90/42.60	                [0 0]     [1]
166.90/42.60	      [a](x0) = [0 0]x0 + [2]
166.90/42.60	     orientation:
166.90/42.60	      a#(b(b(x1))) = [1 1]x1 + [3] >= [0 0]x1 + [2] = a#(a(x1))
166.90/42.60	      
166.90/42.60	      a#(b(b(x1))) = [1 1]x1 + [3] >= [0 0]x1 + [0] = a#(x1)
166.90/42.60	      
166.90/42.60	              [0 0]     [1]    [-& -&]     [1]           
166.90/42.60	      a(x1) = [0 0]x1 + [2] >= [0  0 ]x1 + [2] = b(c(x1))
166.90/42.60	      
166.90/42.60	                    [1 1]     [3]    [1 1]     [3]                 
166.90/42.60	      a(b(b(x1))) = [1 1]x1 + [3] >= [1 1]x1 + [3] = b(b(a(a(x1))))
166.90/42.60	      
166.90/42.60	                 [1 1]     [3]           
166.90/42.60	      b(a(x1)) = [0 0]x1 + [2] >= x1 = x1
166.90/42.60	     problem:
166.90/42.60	      DPs:
166.90/42.60	       
166.90/42.60	      TRS:
166.90/42.60	       a(x1) -> b(c(x1))
166.90/42.60	       a(b(b(x1))) -> b(b(a(a(x1))))
166.90/42.60	       b(a(x1)) -> x1
166.90/42.60	     Qed
166.90/42.60	EOF