165.80/42.39	YES
165.80/42.39	
165.80/42.39	Problem:
165.80/42.39	 a(b(x1)) -> x1
165.80/42.39	 a(c(x1)) -> c(c(x1))
165.80/42.39	 b(c(x1)) -> a(a(b(b(x1))))
165.80/42.39	
165.80/42.39	Proof:
165.80/42.39	 DP Processor:
165.80/42.39	  DPs:
165.80/42.39	   b#(c(x1)) -> b#(x1)
165.80/42.39	   b#(c(x1)) -> b#(b(x1))
165.80/42.39	   b#(c(x1)) -> a#(b(b(x1)))
165.80/42.39	   b#(c(x1)) -> a#(a(b(b(x1))))
165.80/42.39	  TRS:
165.80/42.39	   a(b(x1)) -> x1
165.80/42.39	   a(c(x1)) -> c(c(x1))
165.80/42.39	   b(c(x1)) -> a(a(b(b(x1))))
165.80/42.39	  TDG Processor:
165.80/42.39	   DPs:
165.80/42.39	    b#(c(x1)) -> b#(x1)
165.80/42.39	    b#(c(x1)) -> b#(b(x1))
165.80/42.39	    b#(c(x1)) -> a#(b(b(x1)))
165.80/42.39	    b#(c(x1)) -> a#(a(b(b(x1))))
165.80/42.39	   TRS:
165.80/42.39	    a(b(x1)) -> x1
165.80/42.39	    a(c(x1)) -> c(c(x1))
165.80/42.39	    b(c(x1)) -> a(a(b(b(x1))))
165.80/42.39	   graph:
165.80/42.39	    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(b(b(x1))))
165.80/42.39	    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(b(b(x1)))
165.80/42.39	    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
165.80/42.39	    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
165.80/42.39	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(b(b(x1))))
165.80/42.39	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(b(x1)))
165.80/42.39	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
165.80/42.39	    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
165.80/42.39	   SCC Processor:
165.80/42.39	    #sccs: 1
165.80/42.39	    #rules: 2
165.80/42.39	    #arcs: 8/16
165.80/42.39	    DPs:
165.80/42.39	     b#(c(x1)) -> b#(b(x1))
165.80/42.39	     b#(c(x1)) -> b#(x1)
165.80/42.39	    TRS:
165.80/42.39	     a(b(x1)) -> x1
165.80/42.39	     a(c(x1)) -> c(c(x1))
165.80/42.39	     b(c(x1)) -> a(a(b(b(x1))))
165.80/42.39	    Arctic Interpretation Processor:
165.80/42.39	     dimension: 1
165.80/42.39	     usable rules:
165.80/42.39	      a(b(x1)) -> x1
165.80/42.39	      a(c(x1)) -> c(c(x1))
165.80/42.39	      b(c(x1)) -> a(a(b(b(x1))))
165.80/42.39	     interpretation:
165.80/42.39	      [b#](x0) = x0 + 2,
165.80/42.39	      
165.80/42.39	      [c](x0) = 1x0 + 12,
165.80/42.39	      
165.80/42.39	      [a](x0) = 1x0 + 0,
165.80/42.39	      
165.80/42.39	      [b](x0) = -1x0 + 0
165.80/42.39	     orientation:
165.80/42.39	      b#(c(x1)) = 1x1 + 12 >= -1x1 + 2 = b#(b(x1))
165.80/42.39	      
165.80/42.39	      b#(c(x1)) = 1x1 + 12 >= x1 + 2 = b#(x1)
165.80/42.39	      
165.80/42.39	      a(b(x1)) = x1 + 1 >= x1 = x1
165.80/42.39	      
165.80/42.39	      a(c(x1)) = 2x1 + 13 >= 2x1 + 13 = c(c(x1))
165.80/42.39	      
165.80/42.39	      b(c(x1)) = x1 + 11 >= x1 + 2 = a(a(b(b(x1))))
165.80/42.39	     problem:
165.80/42.39	      DPs:
165.80/42.39	       
165.80/42.39	      TRS:
165.80/42.39	       a(b(x1)) -> x1
165.80/42.39	       a(c(x1)) -> c(c(x1))
165.80/42.39	       b(c(x1)) -> a(a(b(b(x1))))
165.80/42.39	     Qed
165.80/42.40	EOF