174.41/44.51	YES
174.41/44.51	
174.41/44.51	Problem:
174.41/44.51	 a(a(x1)) -> x1
174.41/44.51	 a(b(x1)) -> c(c(x1))
174.41/44.51	 c(b(x1)) -> b(b(a(x1)))
174.41/44.51	
174.41/44.51	Proof:
174.41/44.51	 String Reversal Processor:
174.41/44.51	  a(a(x1)) -> x1
174.41/44.51	  b(a(x1)) -> c(c(x1))
174.41/44.51	  b(c(x1)) -> a(b(b(x1)))
174.41/44.51	  DP Processor:
174.41/44.51	   DPs:
174.41/44.51	    b#(c(x1)) -> b#(x1)
174.41/44.51	    b#(c(x1)) -> b#(b(x1))
174.41/44.51	    b#(c(x1)) -> a#(b(b(x1)))
174.41/44.51	   TRS:
174.41/44.51	    a(a(x1)) -> x1
174.41/44.51	    b(a(x1)) -> c(c(x1))
174.41/44.51	    b(c(x1)) -> a(b(b(x1)))
174.41/44.51	   TDG Processor:
174.41/44.51	    DPs:
174.41/44.51	     b#(c(x1)) -> b#(x1)
174.41/44.51	     b#(c(x1)) -> b#(b(x1))
174.41/44.51	     b#(c(x1)) -> a#(b(b(x1)))
174.41/44.51	    TRS:
174.41/44.51	     a(a(x1)) -> x1
174.41/44.51	     b(a(x1)) -> c(c(x1))
174.41/44.51	     b(c(x1)) -> a(b(b(x1)))
174.41/44.51	    graph:
174.41/44.51	     b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(b(b(x1)))
174.41/44.51	     b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
174.41/44.51	     b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
174.41/44.51	     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(b(b(x1)))
174.41/44.51	     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
174.41/44.51	     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
174.41/44.51	    SCC Processor:
174.41/44.51	     #sccs: 1
174.41/44.51	     #rules: 2
174.41/44.51	     #arcs: 6/9
174.41/44.51	     DPs:
174.41/44.51	      b#(c(x1)) -> b#(b(x1))
174.41/44.51	      b#(c(x1)) -> b#(x1)
174.41/44.51	     TRS:
174.41/44.51	      a(a(x1)) -> x1
174.41/44.51	      b(a(x1)) -> c(c(x1))
174.41/44.51	      b(c(x1)) -> a(b(b(x1)))
174.41/44.51	     Arctic Interpretation Processor:
174.41/44.51	      dimension: 2
174.41/44.51	      usable rules:
174.41/44.51	       a(a(x1)) -> x1
174.41/44.51	       b(a(x1)) -> c(c(x1))
174.41/44.51	       b(c(x1)) -> a(b(b(x1)))
174.41/44.51	      interpretation:
174.41/44.51	       [b#](x0) = [3 2]x0 + [0],
174.41/44.51	       
174.41/44.51	                 [0  1 ]     [1 ]
174.41/44.51	       [c](x0) = [-& 0 ]x0 + [-&],
174.41/44.51	       
174.41/44.51	                 [-& 0 ]     [0]
174.41/44.51	       [b](x0) = [0  -&]x0 + [0],
174.41/44.51	       
174.41/44.51	                 [-& 0 ]     [0]
174.41/44.51	       [a](x0) = [0  1 ]x0 + [1]
174.41/44.51	      orientation:
174.41/44.51	       b#(c(x1)) = [3 4]x1 + [4] >= [2 3]x1 + [3] = b#(b(x1))
174.41/44.51	       
174.41/44.51	       b#(c(x1)) = [3 4]x1 + [4] >= [3 2]x1 + [0] = b#(x1)
174.41/44.51	       
174.41/44.51	                  [0 1]     [1]           
174.41/44.51	       a(a(x1)) = [1 2]x1 + [2] >= x1 = x1
174.41/44.51	       
174.41/44.51	                  [0  1 ]     [1]    [0  1 ]     [1 ]           
174.41/44.51	       b(a(x1)) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [-&] = c(c(x1))
174.41/44.51	       
174.41/44.51	                  [-& 0 ]     [0]    [-& 0 ]     [0]              
174.41/44.51	       b(c(x1)) = [0  1 ]x1 + [1] >= [0  1 ]x1 + [1] = a(b(b(x1)))
174.41/44.51	      problem:
174.41/44.51	       DPs:
174.41/44.51	        b#(c(x1)) -> b#(x1)
174.41/44.51	       TRS:
174.41/44.51	        a(a(x1)) -> x1
174.41/44.51	        b(a(x1)) -> c(c(x1))
174.41/44.51	        b(c(x1)) -> a(b(b(x1)))
174.41/44.51	      Restore Modifier:
174.41/44.51	       DPs:
174.41/44.51	        b#(c(x1)) -> b#(x1)
174.41/44.51	       TRS:
174.41/44.51	        a(a(x1)) -> x1
174.41/44.51	        b(a(x1)) -> c(c(x1))
174.41/44.51	        b(c(x1)) -> a(b(b(x1)))
174.41/44.51	       EDG Processor:
174.41/44.51	        DPs:
174.41/44.51	         b#(c(x1)) -> b#(x1)
174.41/44.51	        TRS:
174.41/44.51	         a(a(x1)) -> x1
174.41/44.51	         b(a(x1)) -> c(c(x1))
174.41/44.51	         b(c(x1)) -> a(b(b(x1)))
174.41/44.51	        graph:
174.41/44.51	         b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
174.41/44.51	        Usable Rule Processor:
174.41/44.51	         DPs:
174.41/44.51	          b#(c(x1)) -> b#(x1)
174.41/44.51	         TRS:
174.41/44.51	          
174.41/44.51	         Arctic Interpretation Processor:
174.41/44.51	          dimension: 4
174.41/44.51	          usable rules:
174.41/44.51	           
174.41/44.51	          interpretation:
174.41/44.51	           [b#](x0) = [0  -& -& -&]x0,
174.41/44.51	           
174.41/44.51	                     [1 0 0 0]     [0]
174.41/44.51	                     [0 0 0 0]     [0]
174.41/44.51	           [c](x0) = [1 0 0 0]x0 + [0]
174.41/44.51	                     [0 0 0 0]     [0]
174.41/44.51	          orientation:
174.41/44.51	           b#(c(x1)) = [1 0 0 0]x1 + [0] >= [0  -& -& -&]x1 = b#(x1)
174.41/44.51	          problem:
174.41/44.51	           DPs:
174.41/44.51	            
174.41/44.51	           TRS:
174.41/44.51	            
174.41/44.51	          Qed
174.41/44.52	EOF