172.76/45.01	YES
172.76/45.02	
172.76/45.02	Problem:
172.76/45.02	 a(x1) -> b(x1)
172.76/45.02	 a(b(x1)) -> x1
172.76/45.02	 c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	
172.76/45.02	Proof:
172.76/45.02	 DP Processor:
172.76/45.02	  DPs:
172.76/45.02	   c#(c(b(x1))) -> c#(x1)
172.76/45.02	   c#(c(b(x1))) -> c#(c(x1))
172.76/45.02	   c#(c(b(x1))) -> a#(c(c(x1)))
172.76/45.02	   c#(c(b(x1))) -> c#(a(c(c(x1))))
172.76/45.02	   c#(c(b(x1))) -> a#(c(a(c(c(x1)))))
172.76/45.02	  TRS:
172.76/45.02	   a(x1) -> b(x1)
172.76/45.02	   a(b(x1)) -> x1
172.76/45.02	   c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	  TDG Processor:
172.76/45.02	   DPs:
172.76/45.02	    c#(c(b(x1))) -> c#(x1)
172.76/45.02	    c#(c(b(x1))) -> c#(c(x1))
172.76/45.02	    c#(c(b(x1))) -> a#(c(c(x1)))
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1))))
172.76/45.02	    c#(c(b(x1))) -> a#(c(a(c(c(x1)))))
172.76/45.02	   TRS:
172.76/45.02	    a(x1) -> b(x1)
172.76/45.02	    a(b(x1)) -> x1
172.76/45.02	    c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	   graph:
172.76/45.02	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(a(c(c(x1)))))
172.76/45.02	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
172.76/45.02	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(c(x1)))
172.76/45.02	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1))
172.76/45.02	    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1)
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1)))) ->
172.76/45.02	    c#(c(b(x1))) -> a#(c(a(c(c(x1)))))
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1)))) ->
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1))))
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> a#(c(c(x1)))
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(c(x1))
172.76/45.02	    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(x1)
172.76/45.02	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(a(c(c(x1)))))
172.76/45.02	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
172.76/45.02	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1)))
172.76/45.02	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1))
172.76/45.02	    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
172.76/45.02	   SCC Processor:
172.76/45.02	    #sccs: 1
172.76/45.02	    #rules: 3
172.76/45.02	    #arcs: 15/25
172.76/45.02	    DPs:
172.76/45.02	     c#(c(b(x1))) -> c#(c(x1))
172.76/45.02	     c#(c(b(x1))) -> c#(x1)
172.76/45.02	     c#(c(b(x1))) -> c#(a(c(c(x1))))
172.76/45.02	    TRS:
172.76/45.02	     a(x1) -> b(x1)
172.76/45.02	     a(b(x1)) -> x1
172.76/45.02	     c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	    Arctic Interpretation Processor:
172.76/45.02	     dimension: 2
172.76/45.02	     usable rules:
172.76/45.02	      a(x1) -> b(x1)
172.76/45.02	      a(b(x1)) -> x1
172.76/45.02	      c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	     interpretation:
172.76/45.02	      [c#](x0) = [0 2]x0 + [3],
172.76/45.02	      
172.76/45.02	                [-& 0 ]     [0]
172.76/45.02	      [c](x0) = [0  -&]x0 + [0],
172.76/45.02	      
172.76/45.02	                [1  0 ]     [2 ]
172.76/45.02	      [b](x0) = [0  -&]x0 + [-&],
172.76/45.02	      
172.76/45.02	                [1  0 ]     [2]
172.76/45.02	      [a](x0) = [0  -&]x0 + [0]
172.76/45.02	     orientation:
172.76/45.02	      c#(c(b(x1))) = [3 2]x1 + [4] >= [2 0]x1 + [3] = c#(c(x1))
172.76/45.02	      
172.76/45.02	      c#(c(b(x1))) = [3 2]x1 + [4] >= [0 2]x1 + [3] = c#(x1)
172.76/45.02	      
172.76/45.02	      c#(c(b(x1))) = [3 2]x1 + [4] >= [2 0]x1 + [3] = c#(a(c(c(x1))))
172.76/45.02	      
172.76/45.02	              [1  0 ]     [2]    [1  0 ]     [2 ]        
172.76/45.02	      a(x1) = [0  -&]x1 + [0] >= [0  -&]x1 + [-&] = b(x1)
172.76/45.02	      
172.76/45.02	                 [2 1]     [3]           
172.76/45.02	      a(b(x1)) = [1 0]x1 + [2] >= x1 = x1
172.76/45.02	      
172.76/45.02	                    [1  0 ]     [2]    [1  0 ]     [2]                    
172.76/45.02	      c(c(b(x1))) = [0  -&]x1 + [0] >= [0  -&]x1 + [0] = a(c(a(c(c(x1)))))
172.76/45.02	     problem:
172.76/45.02	      DPs:
172.76/45.02	       c#(c(b(x1))) -> c#(x1)
172.76/45.02	      TRS:
172.76/45.02	       a(x1) -> b(x1)
172.76/45.02	       a(b(x1)) -> x1
172.76/45.02	       c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	     Restore Modifier:
172.76/45.02	      DPs:
172.76/45.02	       c#(c(b(x1))) -> c#(x1)
172.76/45.02	      TRS:
172.76/45.02	       a(x1) -> b(x1)
172.76/45.02	       a(b(x1)) -> x1
172.76/45.02	       c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	      EDG Processor:
172.76/45.02	       DPs:
172.76/45.02	        c#(c(b(x1))) -> c#(x1)
172.76/45.02	       TRS:
172.76/45.02	        a(x1) -> b(x1)
172.76/45.02	        a(b(x1)) -> x1
172.76/45.02	        c(c(b(x1))) -> a(c(a(c(c(x1)))))
172.76/45.02	       graph:
172.76/45.02	        c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
172.76/45.02	       Usable Rule Processor:
172.76/45.02	        DPs:
172.76/45.02	         c#(c(b(x1))) -> c#(x1)
172.76/45.02	        TRS:
172.76/45.02	         
172.76/45.02	        Arctic Interpretation Processor:
172.76/45.02	         dimension: 1
172.76/45.02	         usable rules:
172.76/45.02	          
172.76/45.02	         interpretation:
172.76/45.02	          [c#](x0) = 6x0,
172.76/45.02	          
172.76/45.02	          [c](x0) = 1x0 + 12,
172.76/45.02	          
172.76/45.02	          [b](x0) = x0 + 9
172.76/45.02	         orientation:
172.76/45.02	          c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1)
172.76/45.02	         problem:
172.76/45.02	          DPs:
172.76/45.02	           
172.76/45.02	          TRS:
172.76/45.02	           
172.76/45.02	         Qed
172.76/45.02	EOF