171.94/43.86	YES
171.94/43.86	
171.94/43.86	Problem:
171.94/43.86	 a(x1) -> b(c(b(c(x1))))
171.94/43.86	 b(b(x1)) -> x1
171.94/43.86	 c(c(b(x1))) -> a(c(x1))
171.94/43.86	
171.94/43.86	Proof:
171.94/43.86	 DP Processor:
171.94/43.86	  DPs:
171.94/43.86	   a#(x1) -> c#(x1)
171.94/43.86	   a#(x1) -> b#(c(x1))
171.94/43.86	   a#(x1) -> c#(b(c(x1)))
171.94/43.86	   a#(x1) -> b#(c(b(c(x1))))
171.94/43.86	   c#(c(b(x1))) -> c#(x1)
171.94/43.86	   c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	  TRS:
171.94/43.86	   a(x1) -> b(c(b(c(x1))))
171.94/43.86	   b(b(x1)) -> x1
171.94/43.86	   c(c(b(x1))) -> a(c(x1))
171.94/43.86	  TDG Processor:
171.94/43.86	   DPs:
171.94/43.86	    a#(x1) -> c#(x1)
171.94/43.86	    a#(x1) -> b#(c(x1))
171.94/43.86	    a#(x1) -> c#(b(c(x1)))
171.94/43.86	    a#(x1) -> b#(c(b(c(x1))))
171.94/43.86	    c#(c(b(x1))) -> c#(x1)
171.94/43.86	    c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	   TRS:
171.94/43.86	    a(x1) -> b(c(b(c(x1))))
171.94/43.86	    b(b(x1)) -> x1
171.94/43.86	    c(c(b(x1))) -> a(c(x1))
171.94/43.86	   graph:
171.94/43.86	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
171.94/43.86	    c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> b#(c(b(c(x1))))
171.94/43.86	    c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> c#(b(c(x1)))
171.94/43.86	    c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> b#(c(x1))
171.94/43.86	    c#(c(b(x1))) -> a#(c(x1)) -> a#(x1) -> c#(x1)
171.94/43.86	    a#(x1) -> c#(b(c(x1))) -> c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	    a#(x1) -> c#(b(c(x1))) -> c#(c(b(x1))) -> c#(x1)
171.94/43.86	    a#(x1) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	    a#(x1) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
171.94/43.86	   SCC Processor:
171.94/43.86	    #sccs: 1
171.94/43.86	    #rules: 4
171.94/43.86	    #arcs: 10/36
171.94/43.86	    DPs:
171.94/43.86	     c#(c(b(x1))) -> c#(x1)
171.94/43.86	     c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	     a#(x1) -> c#(x1)
171.94/43.86	     a#(x1) -> c#(b(c(x1)))
171.94/43.86	    TRS:
171.94/43.86	     a(x1) -> b(c(b(c(x1))))
171.94/43.86	     b(b(x1)) -> x1
171.94/43.86	     c(c(b(x1))) -> a(c(x1))
171.94/43.86	    Arctic Interpretation Processor:
171.94/43.86	     dimension: 2
171.94/43.86	     usable rules:
171.94/43.86	      a(x1) -> b(c(b(c(x1))))
171.94/43.86	      b(b(x1)) -> x1
171.94/43.86	      c(c(b(x1))) -> a(c(x1))
171.94/43.86	     interpretation:
171.94/43.86	      [c#](x0) = [0  -&]x0 + [0],
171.94/43.86	      
171.94/43.86	      [a#](x0) = [1  -&]x0 + [2],
171.94/43.86	      
171.94/43.86	                [-& 0 ]     [0]
171.94/43.86	      [b](x0) = [0  1 ]x0 + [2],
171.94/43.86	      
171.94/43.86	                [-& 0 ]     [1]
171.94/43.86	      [c](x0) = [0  -&]x0 + [0],
171.94/43.86	      
171.94/43.86	                [0  -&]     [0]
171.94/43.86	      [a](x0) = [1  0 ]x0 + [2]
171.94/43.86	     orientation:
171.94/43.86	      c#(c(b(x1))) = [0 1]x1 + [2] >= [0  -&]x1 + [0] = c#(x1)
171.94/43.86	      
171.94/43.86	      c#(c(b(x1))) = [0 1]x1 + [2] >= [-& 1 ]x1 + [2] = a#(c(x1))
171.94/43.86	      
171.94/43.86	      a#(x1) = [1  -&]x1 + [2] >= [0  -&]x1 + [0] = c#(x1)
171.94/43.86	      
171.94/43.86	      a#(x1) = [1  -&]x1 + [2] >= [0  -&]x1 + [0] = c#(b(c(x1)))
171.94/43.86	      
171.94/43.86	              [0  -&]     [0]    [0  -&]     [0]                 
171.94/43.86	      a(x1) = [1  0 ]x1 + [2] >= [1  0 ]x1 + [2] = b(c(b(c(x1))))
171.94/43.86	      
171.94/43.86	                 [0 1]     [2]           
171.94/43.86	      b(b(x1)) = [1 2]x1 + [3] >= x1 = x1
171.94/43.86	      
171.94/43.86	                    [-& 0 ]     [1]    [-& 0 ]     [1]           
171.94/43.86	      c(c(b(x1))) = [0  1 ]x1 + [2] >= [0  1 ]x1 + [2] = a(c(x1))
171.94/43.86	     problem:
171.94/43.86	      DPs:
171.94/43.86	       c#(c(b(x1))) -> c#(x1)
171.94/43.86	       c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	      TRS:
171.94/43.86	       a(x1) -> b(c(b(c(x1))))
171.94/43.86	       b(b(x1)) -> x1
171.94/43.86	       c(c(b(x1))) -> a(c(x1))
171.94/43.86	     Restore Modifier:
171.94/43.86	      DPs:
171.94/43.86	       c#(c(b(x1))) -> c#(x1)
171.94/43.86	       c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	      TRS:
171.94/43.86	       a(x1) -> b(c(b(c(x1))))
171.94/43.86	       b(b(x1)) -> x1
171.94/43.86	       c(c(b(x1))) -> a(c(x1))
171.94/43.86	      EDG Processor:
171.94/43.86	       DPs:
171.94/43.86	        c#(c(b(x1))) -> c#(x1)
171.94/43.86	        c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	       TRS:
171.94/43.86	        a(x1) -> b(c(b(c(x1))))
171.94/43.86	        b(b(x1)) -> x1
171.94/43.86	        c(c(b(x1))) -> a(c(x1))
171.94/43.86	       graph:
171.94/43.86	        c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
171.94/43.86	        c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
171.94/43.86	       SCC Processor:
171.94/43.86	        #sccs: 1
171.94/43.86	        #rules: 1
171.94/43.86	        #arcs: 2/4
171.94/43.86	        DPs:
171.94/43.86	         c#(c(b(x1))) -> c#(x1)
171.94/43.86	        TRS:
171.94/43.86	         a(x1) -> b(c(b(c(x1))))
171.94/43.86	         b(b(x1)) -> x1
171.94/43.86	         c(c(b(x1))) -> a(c(x1))
171.94/43.86	        Usable Rule Processor:
171.94/43.86	         DPs:
171.94/43.86	          c#(c(b(x1))) -> c#(x1)
171.94/43.86	         TRS:
171.94/43.86	          
171.94/43.86	         Arctic Interpretation Processor:
171.94/43.86	          dimension: 1
171.94/43.86	          usable rules:
171.94/43.86	           
171.94/43.86	          interpretation:
171.94/43.86	           [c#](x0) = 6x0,
171.94/43.86	           
171.94/43.86	           [b](x0) = x0 + 9,
171.94/43.86	           
171.94/43.86	           [c](x0) = 1x0 + 12
171.94/43.86	          orientation:
171.94/43.86	           c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1)
171.94/43.86	          problem:
171.94/43.86	           DPs:
171.94/43.86	            
171.94/43.86	           TRS:
171.94/43.86	            
171.94/43.86	          Qed
171.94/43.87	EOF