175.43/44.88	YES
175.43/44.89	
175.43/44.89	Problem:
175.43/44.89	 a(x1) -> b(x1)
175.43/44.89	 a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	 c(c(x1)) -> x1
175.43/44.89	
175.43/44.89	Proof:
175.43/44.89	 DP Processor:
175.43/44.89	  DPs:
175.43/44.89	   a#(b(c(x1))) -> a#(x1)
175.43/44.89	   a#(b(c(x1))) -> a#(a(x1))
175.43/44.89	   a#(b(c(x1))) -> c#(a(a(x1)))
175.43/44.89	   a#(b(c(x1))) -> a#(c(a(a(x1))))
175.43/44.89	   a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.43/44.89	  TRS:
175.43/44.89	   a(x1) -> b(x1)
175.43/44.89	   a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	   c(c(x1)) -> x1
175.43/44.89	  TDG Processor:
175.43/44.89	   DPs:
175.43/44.89	    a#(b(c(x1))) -> a#(x1)
175.43/44.89	    a#(b(c(x1))) -> a#(a(x1))
175.43/44.89	    a#(b(c(x1))) -> c#(a(a(x1)))
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1))))
175.43/44.89	    a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.43/44.89	   TRS:
175.43/44.89	    a(x1) -> b(x1)
175.43/44.89	    a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	    c(c(x1)) -> x1
175.43/44.89	   graph:
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1)))) ->
175.43/44.89	    a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1)))) ->
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1))))
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(b(c(x1))) -> c#(a(a(x1)))
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(b(c(x1))) -> a#(a(x1))
175.43/44.89	    a#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(b(c(x1))) -> a#(x1)
175.43/44.89	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.43/44.89	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(c(a(a(x1))))
175.43/44.89	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(a(a(x1)))
175.43/44.89	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1))
175.43/44.89	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(x1)
175.43/44.89	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.43/44.89	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(c(a(a(x1))))
175.43/44.89	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(a(a(x1)))
175.43/44.89	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(a(x1))
175.43/44.89	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
175.43/44.89	   SCC Processor:
175.43/44.89	    #sccs: 1
175.43/44.89	    #rules: 3
175.43/44.89	    #arcs: 15/25
175.43/44.89	    DPs:
175.43/44.89	     a#(b(c(x1))) -> a#(c(a(a(x1))))
175.43/44.89	     a#(b(c(x1))) -> a#(x1)
175.43/44.89	     a#(b(c(x1))) -> a#(a(x1))
175.43/44.89	    TRS:
175.43/44.89	     a(x1) -> b(x1)
175.43/44.89	     a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	     c(c(x1)) -> x1
175.43/44.89	    Arctic Interpretation Processor:
175.43/44.89	     dimension: 2
175.43/44.89	     usable rules:
175.43/44.89	      a(x1) -> b(x1)
175.43/44.89	      a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	      c(c(x1)) -> x1
175.43/44.89	     interpretation:
175.43/44.89	      [a#](x0) = [-& 0 ]x0 + [0],
175.43/44.89	      
175.43/44.89	                [1  0 ]     [3]
175.43/44.89	      [c](x0) = [0  -&]x0 + [2],
175.43/44.89	      
175.43/44.89	                [-& 0 ]     [0 ]
175.43/44.89	      [b](x0) = [0  -&]x0 + [-&],
175.43/44.89	      
175.43/44.89	                [-& 0 ]     [0]
175.43/44.89	      [a](x0) = [0  -&]x0 + [0]
175.43/44.89	     orientation:
175.43/44.89	      a#(b(c(x1))) = [1 0]x1 + [3] >= [0  -&]x1 + [2] = a#(c(a(a(x1))))
175.43/44.89	      
175.43/44.89	      a#(b(c(x1))) = [1 0]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1)
175.43/44.89	      
175.43/44.89	      a#(b(c(x1))) = [1 0]x1 + [3] >= [0  -&]x1 + [0] = a#(a(x1))
175.43/44.89	      
175.43/44.89	              [-& 0 ]     [0]    [-& 0 ]     [0 ]        
175.43/44.89	      a(x1) = [0  -&]x1 + [0] >= [0  -&]x1 + [-&] = b(x1)
175.43/44.89	      
175.43/44.89	                    [1  0 ]     [3]    [1  0 ]     [3]                    
175.43/44.89	      a(b(c(x1))) = [0  -&]x1 + [2] >= [0  -&]x1 + [2] = c(a(c(a(a(x1)))))
175.43/44.89	      
175.43/44.89	                 [2 1]     [4]           
175.43/44.89	      c(c(x1)) = [1 0]x1 + [3] >= x1 = x1
175.43/44.89	     problem:
175.43/44.89	      DPs:
175.43/44.89	       a#(b(c(x1))) -> a#(x1)
175.43/44.89	      TRS:
175.43/44.89	       a(x1) -> b(x1)
175.43/44.89	       a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	       c(c(x1)) -> x1
175.43/44.89	     Restore Modifier:
175.43/44.89	      DPs:
175.43/44.89	       a#(b(c(x1))) -> a#(x1)
175.43/44.89	      TRS:
175.43/44.89	       a(x1) -> b(x1)
175.43/44.89	       a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	       c(c(x1)) -> x1
175.43/44.89	      EDG Processor:
175.43/44.89	       DPs:
175.43/44.89	        a#(b(c(x1))) -> a#(x1)
175.43/44.89	       TRS:
175.43/44.89	        a(x1) -> b(x1)
175.43/44.89	        a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.43/44.89	        c(c(x1)) -> x1
175.43/44.89	       graph:
175.43/44.89	        a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
175.43/44.89	       Usable Rule Processor:
175.43/44.89	        DPs:
175.43/44.89	         a#(b(c(x1))) -> a#(x1)
175.43/44.89	        TRS:
175.43/44.89	         
175.43/44.89	        Arctic Interpretation Processor:
175.43/44.89	         dimension: 1
175.43/44.89	         usable rules:
175.43/44.89	          
175.43/44.89	         interpretation:
175.43/44.89	          [a#](x0) = 6x0,
175.43/44.89	          
175.43/44.89	          [c](x0) = x0 + 9,
175.43/44.89	          
175.43/44.89	          [b](x0) = 1x0 + 12
175.43/44.89	         orientation:
175.43/44.89	          a#(b(c(x1))) = 7x1 + 18 >= 6x1 = a#(x1)
175.43/44.89	         problem:
175.43/44.89	          DPs:
175.43/44.89	           
175.43/44.89	          TRS:
175.43/44.89	           
175.43/44.89	         Qed
175.67/44.90	EOF