174.86/44.69	YES
174.86/44.70	
174.86/44.70	Problem:
174.86/44.70	 a(x1) -> b(x1)
174.86/44.70	 b(b(x1)) -> x1
174.86/44.70	 b(c(c(x1))) -> c(c(a(c(b(x1)))))
174.86/44.70	
174.86/44.70	Proof:
174.86/44.70	 String Reversal Processor:
174.86/44.70	  a(x1) -> b(x1)
174.86/44.70	  b(b(x1)) -> x1
174.86/44.70	  c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	  DP Processor:
174.86/44.70	   DPs:
174.86/44.70	    a#(x1) -> b#(x1)
174.86/44.70	    c#(c(b(x1))) -> c#(x1)
174.86/44.70	    c#(c(b(x1))) -> c#(c(x1))
174.86/44.70	    c#(c(b(x1))) -> a#(c(c(x1)))
174.86/44.70	    c#(c(b(x1))) -> c#(a(c(c(x1))))
174.86/44.70	    c#(c(b(x1))) -> b#(c(a(c(c(x1)))))
174.86/44.70	   TRS:
174.86/44.70	    a(x1) -> b(x1)
174.86/44.70	    b(b(x1)) -> x1
174.86/44.70	    c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	   TDG Processor:
174.86/44.70	    DPs:
174.86/44.70	     a#(x1) -> b#(x1)
174.86/44.70	     c#(c(b(x1))) -> c#(x1)
174.86/44.70	     c#(c(b(x1))) -> c#(c(x1))
174.86/44.70	     c#(c(b(x1))) -> a#(c(c(x1)))
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1))))
174.86/44.70	     c#(c(b(x1))) -> b#(c(a(c(c(x1)))))
174.86/44.70	    TRS:
174.86/44.70	     a(x1) -> b(x1)
174.86/44.70	     b(b(x1)) -> x1
174.86/44.70	     c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	    graph:
174.86/44.70	     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(c(a(c(c(x1)))))
174.86/44.70	     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
174.86/44.70	     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(c(x1)))
174.86/44.70	     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1))
174.86/44.70	     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1)
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1)))) ->
174.86/44.70	     c#(c(b(x1))) -> b#(c(a(c(c(x1)))))
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1)))) ->
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1))))
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> a#(c(c(x1)))
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(c(x1))
174.86/44.70	     c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(x1)
174.86/44.70	     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(c(a(c(c(x1)))))
174.86/44.70	     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
174.86/44.70	     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1)))
174.86/44.70	     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1))
174.86/44.70	     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
174.86/44.70	     c#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> b#(x1)
174.86/44.70	    SCC Processor:
174.86/44.70	     #sccs: 1
174.86/44.70	     #rules: 3
174.86/44.70	     #arcs: 16/36
174.86/44.70	     DPs:
174.86/44.70	      c#(c(b(x1))) -> c#(c(x1))
174.86/44.70	      c#(c(b(x1))) -> c#(x1)
174.86/44.70	      c#(c(b(x1))) -> c#(a(c(c(x1))))
174.86/44.70	     TRS:
174.86/44.70	      a(x1) -> b(x1)
174.86/44.70	      b(b(x1)) -> x1
174.86/44.70	      c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	     Arctic Interpretation Processor:
174.86/44.70	      dimension: 2
174.86/44.70	      usable rules:
174.86/44.70	       a(x1) -> b(x1)
174.86/44.70	       b(b(x1)) -> x1
174.86/44.70	       c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	      interpretation:
174.86/44.70	       [c#](x0) = [0  -&]x0 + [0],
174.86/44.70	       
174.86/44.70	                 [-& 0 ]     [0]
174.86/44.70	       [c](x0) = [0  -&]x0 + [1],
174.86/44.70	       
174.86/44.70	                 [-& 0 ]     [0]
174.86/44.70	       [b](x0) = [0  1 ]x0 + [3],
174.86/44.70	       
174.86/44.70	                 [-& 0 ]     [1]
174.86/44.70	       [a](x0) = [0  1 ]x0 + [3]
174.86/44.70	      orientation:
174.86/44.70	       c#(c(b(x1))) = [0 1]x1 + [3] >= [-& 0 ]x1 + [0] = c#(c(x1))
174.86/44.70	       
174.86/44.70	       c#(c(b(x1))) = [0 1]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
174.86/44.70	       
174.86/44.70	       c#(c(b(x1))) = [0 1]x1 + [3] >= [-& 0 ]x1 + [1] = c#(a(c(c(x1))))
174.86/44.70	       
174.86/44.70	               [-& 0 ]     [1]    [-& 0 ]     [0]        
174.86/44.70	       a(x1) = [0  1 ]x1 + [3] >= [0  1 ]x1 + [3] = b(x1)
174.86/44.70	       
174.86/44.70	                  [0 1]     [3]           
174.86/44.70	       b(b(x1)) = [1 2]x1 + [4] >= x1 = x1
174.86/44.70	       
174.86/44.70	                     [-& 0 ]     [1]    [-& 0 ]     [1]                    
174.86/44.70	       c(c(b(x1))) = [0  1 ]x1 + [3] >= [0  1 ]x1 + [3] = b(c(a(c(c(x1)))))
174.86/44.70	      problem:
174.86/44.70	       DPs:
174.86/44.70	        c#(c(b(x1))) -> c#(x1)
174.86/44.70	       TRS:
174.86/44.70	        a(x1) -> b(x1)
174.86/44.70	        b(b(x1)) -> x1
174.86/44.70	        c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	      Restore Modifier:
174.86/44.70	       DPs:
174.86/44.70	        c#(c(b(x1))) -> c#(x1)
174.86/44.70	       TRS:
174.86/44.70	        a(x1) -> b(x1)
174.86/44.70	        b(b(x1)) -> x1
174.86/44.70	        c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	       EDG Processor:
174.86/44.70	        DPs:
174.86/44.70	         c#(c(b(x1))) -> c#(x1)
174.86/44.70	        TRS:
174.86/44.70	         a(x1) -> b(x1)
174.86/44.70	         b(b(x1)) -> x1
174.86/44.70	         c(c(b(x1))) -> b(c(a(c(c(x1)))))
174.86/44.70	        graph:
174.86/44.70	         c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
174.86/44.70	        Usable Rule Processor:
174.86/44.70	         DPs:
174.86/44.70	          c#(c(b(x1))) -> c#(x1)
174.86/44.70	         TRS:
174.86/44.70	          
174.86/44.70	         Arctic Interpretation Processor:
174.86/44.70	          dimension: 1
174.86/44.70	          usable rules:
174.86/44.70	           
174.86/44.70	          interpretation:
174.86/44.70	           [c#](x0) = 6x0,
174.86/44.70	           
174.86/44.70	           [c](x0) = 1x0 + 12,
174.86/44.70	           
174.86/44.70	           [b](x0) = x0 + 9
174.86/44.70	          orientation:
174.86/44.70	           c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1)
174.86/44.70	          problem:
174.86/44.70	           DPs:
174.86/44.70	            
174.86/44.70	           TRS:
174.86/44.70	            
174.86/44.70	          Qed
174.86/44.71	EOF