163.66/41.81	YES
163.66/41.82	
163.66/41.82	Problem:
163.66/41.82	 a(b(x1)) -> x1
163.66/41.82	 a(c(x1)) -> b(c(c(a(a(b(x1))))))
163.66/41.82	 b(c(x1)) -> x1
163.66/41.82	
163.66/41.82	Proof:
163.66/41.82	 DP Processor:
163.66/41.82	  DPs:
163.66/41.82	   a#(c(x1)) -> b#(x1)
163.66/41.82	   a#(c(x1)) -> a#(b(x1))
163.66/41.82	   a#(c(x1)) -> a#(a(b(x1)))
163.66/41.82	   a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
163.66/41.82	  TRS:
163.66/41.82	   a(b(x1)) -> x1
163.66/41.82	   a(c(x1)) -> b(c(c(a(a(b(x1))))))
163.66/41.82	   b(c(x1)) -> x1
163.66/41.82	  TDG Processor:
163.66/41.82	   DPs:
163.66/41.82	    a#(c(x1)) -> b#(x1)
163.66/41.82	    a#(c(x1)) -> a#(b(x1))
163.66/41.82	    a#(c(x1)) -> a#(a(b(x1)))
163.66/41.82	    a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
163.66/41.82	   TRS:
163.66/41.82	    a(b(x1)) -> x1
163.66/41.82	    a(c(x1)) -> b(c(c(a(a(b(x1))))))
163.66/41.82	    b(c(x1)) -> x1
163.66/41.82	   graph:
163.66/41.82	    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
163.66/41.82	    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> a#(a(b(x1)))
163.66/41.82	    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> a#(b(x1))
163.66/41.82	    a#(c(x1)) -> a#(a(b(x1))) -> a#(c(x1)) -> b#(x1)
163.66/41.82	    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(c(c(a(a(b(x1))))))
163.66/41.82	    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(a(b(x1)))
163.66/41.82	    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> a#(b(x1))
163.66/41.82	    a#(c(x1)) -> a#(b(x1)) -> a#(c(x1)) -> b#(x1)
163.66/41.82	   SCC Processor:
163.66/41.82	    #sccs: 1
163.66/41.82	    #rules: 2
163.66/41.82	    #arcs: 8/16
163.66/41.82	    DPs:
163.66/41.82	     a#(c(x1)) -> a#(a(b(x1)))
163.66/41.82	     a#(c(x1)) -> a#(b(x1))
163.66/41.82	    TRS:
163.66/41.82	     a(b(x1)) -> x1
163.66/41.82	     a(c(x1)) -> b(c(c(a(a(b(x1))))))
163.66/41.82	     b(c(x1)) -> x1
163.66/41.82	    Arctic Interpretation Processor:
163.66/41.82	     dimension: 1
163.66/41.82	     usable rules:
163.66/41.82	      a(b(x1)) -> x1
163.66/41.82	      a(c(x1)) -> b(c(c(a(a(b(x1))))))
163.66/41.82	      b(c(x1)) -> x1
163.66/41.82	     interpretation:
163.66/41.82	      [a#](x0) = x0 + 0,
163.66/41.82	      
163.66/41.82	      [c](x0) = 1x0 + 10,
163.66/41.82	      
163.66/41.82	      [a](x0) = 1x0 + 0,
163.66/41.82	      
163.66/41.82	      [b](x0) = -1x0 + 1
163.66/41.82	     orientation:
163.66/41.82	      a#(c(x1)) = 1x1 + 10 >= x1 + 2 = a#(a(b(x1)))
163.66/41.82	      
163.66/41.82	      a#(c(x1)) = 1x1 + 10 >= -1x1 + 1 = a#(b(x1))
163.66/41.82	      
163.66/41.82	      a(b(x1)) = x1 + 2 >= x1 = x1
163.66/41.82	      
163.66/41.82	      a(c(x1)) = 2x1 + 11 >= 2x1 + 10 = b(c(c(a(a(b(x1))))))
163.66/41.82	      
163.66/41.82	      b(c(x1)) = x1 + 9 >= x1 = x1
163.66/41.82	     problem:
163.66/41.82	      DPs:
163.66/41.82	       
163.66/41.82	      TRS:
163.66/41.82	       a(b(x1)) -> x1
163.66/41.82	       a(c(x1)) -> b(c(c(a(a(b(x1))))))
163.66/41.82	       b(c(x1)) -> x1
163.66/41.82	     Qed
163.90/41.82	EOF