175.55/44.88	YES
175.55/44.88	
175.55/44.88	Problem:
175.55/44.88	 a(x1) -> b(x1)
175.55/44.88	 a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	 c(x1) -> b(x1)
175.55/44.88	
175.55/44.88	Proof:
175.55/44.88	 DP Processor:
175.55/44.88	  DPs:
175.55/44.88	   a#(b(c(x1))) -> a#(x1)
175.55/44.88	   a#(b(c(x1))) -> a#(a(x1))
175.55/44.88	   a#(b(c(x1))) -> c#(a(a(x1)))
175.55/44.88	   a#(b(c(x1))) -> a#(c(a(a(x1))))
175.55/44.88	   a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.55/44.88	  TRS:
175.55/44.88	   a(x1) -> b(x1)
175.55/44.88	   a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	   c(x1) -> b(x1)
175.55/44.88	  TDG Processor:
175.55/44.88	   DPs:
175.55/44.88	    a#(b(c(x1))) -> a#(x1)
175.55/44.88	    a#(b(c(x1))) -> a#(a(x1))
175.55/44.88	    a#(b(c(x1))) -> c#(a(a(x1)))
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1))))
175.55/44.88	    a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.55/44.88	   TRS:
175.55/44.88	    a(x1) -> b(x1)
175.55/44.88	    a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	    c(x1) -> b(x1)
175.55/44.88	   graph:
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1)))) ->
175.55/44.88	    a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1)))) ->
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1))))
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(b(c(x1))) -> c#(a(a(x1)))
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(b(c(x1))) -> a#(a(x1))
175.55/44.88	    a#(b(c(x1))) -> a#(c(a(a(x1)))) -> a#(b(c(x1))) -> a#(x1)
175.55/44.88	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.55/44.88	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(c(a(a(x1))))
175.55/44.88	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(a(a(x1)))
175.55/44.88	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1))
175.55/44.88	    a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(x1)
175.55/44.88	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(a(c(a(a(x1)))))
175.55/44.88	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(c(a(a(x1))))
175.55/44.88	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(a(a(x1)))
175.55/44.88	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(a(x1))
175.55/44.88	    a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
175.55/44.88	   SCC Processor:
175.55/44.88	    #sccs: 1
175.55/44.88	    #rules: 3
175.55/44.88	    #arcs: 15/25
175.55/44.88	    DPs:
175.55/44.88	     a#(b(c(x1))) -> a#(c(a(a(x1))))
175.55/44.88	     a#(b(c(x1))) -> a#(x1)
175.55/44.88	     a#(b(c(x1))) -> a#(a(x1))
175.55/44.88	    TRS:
175.55/44.88	     a(x1) -> b(x1)
175.55/44.88	     a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	     c(x1) -> b(x1)
175.55/44.88	    Arctic Interpretation Processor:
175.55/44.88	     dimension: 2
175.55/44.88	     usable rules:
175.55/44.88	      a(x1) -> b(x1)
175.55/44.88	      a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	      c(x1) -> b(x1)
175.55/44.88	     interpretation:
175.55/44.88	      [a#](x0) = [1 0]x0 + [2],
175.55/44.88	      
175.55/44.88	                [-& 0 ]     [1]
175.55/44.88	      [c](x0) = [0  2 ]x0 + [3],
175.55/44.88	      
175.55/44.88	                [-& 0 ]     [0 ]
175.55/44.88	      [b](x0) = [0  -&]x0 + [-&],
175.55/44.88	      
175.55/44.88	                [-& 0 ]     [0]
175.55/44.88	      [a](x0) = [0  -&]x0 + [1]
175.55/44.88	     orientation:
175.55/44.88	      a#(b(c(x1))) = [1 3]x1 + [4] >= [0 2]x1 + [3] = a#(c(a(a(x1))))
175.55/44.88	      
175.55/44.88	      a#(b(c(x1))) = [1 3]x1 + [4] >= [1 0]x1 + [2] = a#(x1)
175.55/44.88	      
175.55/44.88	      a#(b(c(x1))) = [1 3]x1 + [4] >= [0 1]x1 + [2] = a#(a(x1))
175.55/44.88	      
175.55/44.88	              [-& 0 ]     [0]    [-& 0 ]     [0 ]        
175.55/44.88	      a(x1) = [0  -&]x1 + [1] >= [0  -&]x1 + [-&] = b(x1)
175.55/44.88	      
175.55/44.88	                    [-& 0 ]     [1]    [-& 0 ]     [1]                    
175.55/44.88	      a(b(c(x1))) = [0  2 ]x1 + [3] >= [0  2 ]x1 + [3] = c(a(c(a(a(x1)))))
175.55/44.88	      
175.55/44.88	              [-& 0 ]     [1]    [-& 0 ]     [0 ]        
175.55/44.88	      c(x1) = [0  2 ]x1 + [3] >= [0  -&]x1 + [-&] = b(x1)
175.55/44.88	     problem:
175.55/44.88	      DPs:
175.55/44.88	       a#(b(c(x1))) -> a#(x1)
175.55/44.88	      TRS:
175.55/44.88	       a(x1) -> b(x1)
175.55/44.88	       a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	       c(x1) -> b(x1)
175.55/44.88	     Restore Modifier:
175.55/44.88	      DPs:
175.55/44.88	       a#(b(c(x1))) -> a#(x1)
175.55/44.88	      TRS:
175.55/44.88	       a(x1) -> b(x1)
175.55/44.88	       a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	       c(x1) -> b(x1)
175.55/44.88	      EDG Processor:
175.55/44.88	       DPs:
175.55/44.88	        a#(b(c(x1))) -> a#(x1)
175.55/44.88	       TRS:
175.55/44.88	        a(x1) -> b(x1)
175.55/44.88	        a(b(c(x1))) -> c(a(c(a(a(x1)))))
175.55/44.88	        c(x1) -> b(x1)
175.55/44.88	       graph:
175.55/44.88	        a#(b(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(x1)
175.55/44.88	       Usable Rule Processor:
175.55/44.88	        DPs:
175.55/44.88	         a#(b(c(x1))) -> a#(x1)
175.55/44.88	        TRS:
175.55/44.88	         
175.55/44.88	        Arctic Interpretation Processor:
175.55/44.88	         dimension: 1
175.55/44.88	         usable rules:
175.55/44.88	          
175.55/44.88	         interpretation:
175.55/44.88	          [a#](x0) = 6x0,
175.55/44.88	          
175.55/44.88	          [c](x0) = x0 + 9,
175.55/44.88	          
175.55/44.88	          [b](x0) = 1x0 + 12
175.55/44.88	         orientation:
175.55/44.88	          a#(b(c(x1))) = 7x1 + 18 >= 6x1 = a#(x1)
175.55/44.88	         problem:
175.55/44.88	          DPs:
175.55/44.88	           
175.55/44.88	          TRS:
175.55/44.88	           
175.55/44.88	         Qed
175.75/44.89	EOF