178.06/45.53	YES
178.06/45.53	
178.06/45.53	Problem:
178.06/45.53	 a(x1) -> b(x1)
178.06/45.53	 a(b(x1)) -> x1
178.06/45.53	 c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.53	
178.06/45.53	Proof:
178.06/45.53	 DP Processor:
178.06/45.53	  DPs:
178.06/45.53	   c#(c(a(x1))) -> c#(x1)
178.06/45.53	   c#(c(a(x1))) -> c#(c(x1))
178.06/45.53	   c#(c(a(x1))) -> a#(c(c(x1)))
178.06/45.53	   c#(c(a(x1))) -> c#(a(c(c(x1))))
178.06/45.53	   c#(c(a(x1))) -> a#(c(a(c(c(x1)))))
178.06/45.53	  TRS:
178.06/45.53	   a(x1) -> b(x1)
178.06/45.53	   a(b(x1)) -> x1
178.06/45.53	   c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.53	  TDG Processor:
178.06/45.53	   DPs:
178.06/45.53	    c#(c(a(x1))) -> c#(x1)
178.06/45.53	    c#(c(a(x1))) -> c#(c(x1))
178.06/45.53	    c#(c(a(x1))) -> a#(c(c(x1)))
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1))))
178.06/45.53	    c#(c(a(x1))) -> a#(c(a(c(c(x1)))))
178.06/45.53	   TRS:
178.06/45.53	    a(x1) -> b(x1)
178.06/45.53	    a(b(x1)) -> x1
178.06/45.53	    c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.53	   graph:
178.06/45.53	    c#(c(a(x1))) -> c#(c(x1)) -> c#(c(a(x1))) -> a#(c(a(c(c(x1)))))
178.06/45.53	    c#(c(a(x1))) -> c#(c(x1)) -> c#(c(a(x1))) -> c#(a(c(c(x1))))
178.06/45.53	    c#(c(a(x1))) -> c#(c(x1)) -> c#(c(a(x1))) -> a#(c(c(x1)))
178.06/45.53	    c#(c(a(x1))) -> c#(c(x1)) -> c#(c(a(x1))) -> c#(c(x1))
178.06/45.53	    c#(c(a(x1))) -> c#(c(x1)) -> c#(c(a(x1))) -> c#(x1)
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1)))) ->
178.06/45.53	    c#(c(a(x1))) -> a#(c(a(c(c(x1)))))
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1)))) ->
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1))))
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(a(x1))) -> a#(c(c(x1)))
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(a(x1))) -> c#(c(x1))
178.06/45.53	    c#(c(a(x1))) -> c#(a(c(c(x1)))) -> c#(c(a(x1))) -> c#(x1)
178.06/45.53	    c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> a#(c(a(c(c(x1)))))
178.06/45.53	    c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(a(c(c(x1))))
178.06/45.53	    c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> a#(c(c(x1)))
178.06/45.53	    c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(c(x1))
178.06/45.53	    c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(x1)
178.06/45.53	   SCC Processor:
178.06/45.53	    #sccs: 1
178.06/45.53	    #rules: 3
178.06/45.53	    #arcs: 15/25
178.06/45.53	    DPs:
178.06/45.53	     c#(c(a(x1))) -> c#(c(x1))
178.06/45.53	     c#(c(a(x1))) -> c#(x1)
178.06/45.53	     c#(c(a(x1))) -> c#(a(c(c(x1))))
178.06/45.53	    TRS:
178.06/45.53	     a(x1) -> b(x1)
178.06/45.53	     a(b(x1)) -> x1
178.06/45.53	     c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.53	    Arctic Interpretation Processor:
178.06/45.53	     dimension: 2
178.06/45.53	     usable rules:
178.06/45.53	      a(x1) -> b(x1)
178.06/45.53	      a(b(x1)) -> x1
178.06/45.53	      c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.53	     interpretation:
178.06/45.53	      [c#](x0) = [1 0]x0 + [0],
178.06/45.53	      
178.06/45.53	                [-& 0 ]     [0]
178.06/45.53	      [c](x0) = [0  -&]x0 + [1],
178.06/45.53	      
178.06/45.53	                [-& 0 ]     [0]
178.06/45.53	      [b](x0) = [0  0 ]x0 + [2],
178.06/45.53	      
178.06/45.53	                [-& 0 ]     [1]
178.06/45.53	      [a](x0) = [0  1 ]x0 + [2]
178.06/45.53	     orientation:
178.06/45.53	      c#(c(a(x1))) = [1 2]x1 + [3] >= [0 1]x1 + [1] = c#(c(x1))
178.06/45.53	      
178.06/45.53	      c#(c(a(x1))) = [1 2]x1 + [3] >= [1 0]x1 + [0] = c#(x1)
178.06/45.53	      
178.06/45.53	      c#(c(a(x1))) = [1 2]x1 + [3] >= [0 1]x1 + [2] = c#(a(c(c(x1))))
178.06/45.53	      
178.06/45.53	              [-& 0 ]     [1]    [-& 0 ]     [0]        
178.06/45.53	      a(x1) = [0  1 ]x1 + [2] >= [0  0 ]x1 + [2] = b(x1)
178.06/45.53	      
178.06/45.53	                 [0 0]     [2]           
178.06/45.53	      a(b(x1)) = [1 1]x1 + [3] >= x1 = x1
178.06/45.53	      
178.06/45.53	                    [-& 0 ]     [1]    [-& 0 ]     [1]                    
178.06/45.53	      c(c(a(x1))) = [0  1 ]x1 + [2] >= [0  1 ]x1 + [2] = a(c(a(c(c(x1)))))
178.06/45.53	     problem:
178.06/45.53	      DPs:
178.06/45.53	       c#(c(a(x1))) -> c#(x1)
178.06/45.53	      TRS:
178.06/45.53	       a(x1) -> b(x1)
178.06/45.53	       a(b(x1)) -> x1
178.06/45.53	       c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.53	     Restore Modifier:
178.06/45.53	      DPs:
178.06/45.53	       c#(c(a(x1))) -> c#(x1)
178.06/45.53	      TRS:
178.06/45.54	       a(x1) -> b(x1)
178.06/45.54	       a(b(x1)) -> x1
178.06/45.54	       c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.54	      EDG Processor:
178.06/45.54	       DPs:
178.06/45.54	        c#(c(a(x1))) -> c#(x1)
178.06/45.54	       TRS:
178.06/45.54	        a(x1) -> b(x1)
178.06/45.54	        a(b(x1)) -> x1
178.06/45.54	        c(c(a(x1))) -> a(c(a(c(c(x1)))))
178.06/45.54	       graph:
178.06/45.54	        c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(x1)
178.06/45.54	       Usable Rule Processor:
178.06/45.54	        DPs:
178.06/45.54	         c#(c(a(x1))) -> c#(x1)
178.06/45.54	        TRS:
178.06/45.54	         
178.06/45.54	        Arctic Interpretation Processor:
178.06/45.54	         dimension: 1
178.06/45.54	         usable rules:
178.06/45.54	          
178.06/45.54	         interpretation:
178.06/45.54	          [c#](x0) = 6x0,
178.06/45.54	          
178.06/45.54	          [c](x0) = 1x0 + 12,
178.06/45.54	          
178.06/45.54	          [a](x0) = x0 + 9
178.06/45.54	         orientation:
178.06/45.54	          c#(c(a(x1))) = 7x1 + 18 >= 6x1 = c#(x1)
178.06/45.54	         problem:
178.06/45.54	          DPs:
178.06/45.54	           
178.06/45.54	          TRS:
178.06/45.54	           
178.06/45.54	         Qed
178.06/45.54	EOF