167.21/42.78	YES
167.21/42.78	
167.21/42.78	Problem:
167.21/42.78	 a(a(b(x1))) -> c(a(c(a(a(x1)))))
167.21/42.78	 a(c(x1)) -> b(a(x1))
167.21/42.78	
167.21/42.78	Proof:
167.21/42.78	 String Reversal Processor:
167.21/42.78	  b(a(a(x1))) -> a(a(c(a(c(x1)))))
167.21/42.78	  c(a(x1)) -> a(b(x1))
167.21/42.78	  DP Processor:
167.21/42.78	   DPs:
167.21/42.78	    b#(a(a(x1))) -> c#(x1)
167.21/42.78	    b#(a(a(x1))) -> c#(a(c(x1)))
167.21/42.78	    c#(a(x1)) -> b#(x1)
167.21/42.78	   TRS:
167.21/42.78	    b(a(a(x1))) -> a(a(c(a(c(x1)))))
167.21/42.78	    c(a(x1)) -> a(b(x1))
167.21/42.78	   TDG Processor:
167.21/42.78	    DPs:
167.21/42.78	     b#(a(a(x1))) -> c#(x1)
167.21/42.78	     b#(a(a(x1))) -> c#(a(c(x1)))
167.21/42.78	     c#(a(x1)) -> b#(x1)
167.21/42.78	    TRS:
167.21/42.78	     b(a(a(x1))) -> a(a(c(a(c(x1)))))
167.21/42.78	     c(a(x1)) -> a(b(x1))
167.21/42.78	    graph:
167.21/42.78	     c#(a(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(a(c(x1)))
167.21/42.78	     c#(a(x1)) -> b#(x1) -> b#(a(a(x1))) -> c#(x1)
167.21/42.78	     b#(a(a(x1))) -> c#(a(c(x1))) -> c#(a(x1)) -> b#(x1)
167.21/42.78	     b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> b#(x1)
167.21/42.78	    Matrix Interpretation Processor: dim=4
167.21/42.78	     
167.21/42.78	     interpretation:
167.21/42.78	      [c#](x0) = [0 0 0 1]x0,
167.21/42.78	      
167.21/42.78	      [b#](x0) = [0 0 1 0]x0,
167.21/42.78	      
167.21/42.78	                [0 0 0 0]     [0]
167.21/42.78	                [0 0 0 1]     [1]
167.21/42.78	      [c](x0) = [0 0 0 1]x0 + [0]
167.21/42.78	                [0 0 0 1]     [0],
167.21/42.78	      
167.21/42.78	                [0 0 0 0]     [0]
167.21/42.78	                [0 0 0 1]     [1]
167.21/42.78	      [a](x0) = [0 1 0 0]x0 + [0]
167.21/42.78	                [0 0 1 0]     [0],
167.21/42.78	      
167.21/42.78	                [0 0 1 1]  
167.21/42.78	                [0 0 1 0]  
167.21/42.78	      [b](x0) = [0 0 1 0]x0
167.21/42.78	                [0 0 1 0]  
167.21/42.78	     orientation:
167.21/42.78	      b#(a(a(x1))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = c#(x1)
167.21/42.78	      
167.21/42.78	      b#(a(a(x1))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = c#(a(c(x1)))
167.21/42.78	      
167.21/42.78	      c#(a(x1)) = [0 0 1 0]x1 >= [0 0 1 0]x1 = b#(x1)
167.21/42.78	      
167.21/42.78	                    [0 1 0 1]     [1]    [0 0 0 0]     [0]                    
167.21/42.78	                    [0 0 0 1]     [1]    [0 0 0 1]     [1]                    
167.21/42.78	      b(a(a(x1))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = a(a(c(a(c(x1)))))
167.21/42.78	                    [0 0 0 1]     [1]    [0 0 0 1]     [1]                    
167.21/42.78	      
167.21/42.78	                 [0 0 0 0]     [0]    [0 0 0 0]     [0]           
167.21/42.78	                 [0 0 1 0]     [1]    [0 0 1 0]     [1]           
167.21/42.78	      c(a(x1)) = [0 0 1 0]x1 + [0] >= [0 0 1 0]x1 + [0] = a(b(x1))
167.21/42.78	                 [0 0 1 0]     [0]    [0 0 1 0]     [0]           
167.21/42.78	     problem:
167.21/42.78	      DPs:
167.21/42.78	       c#(a(x1)) -> b#(x1)
167.21/42.78	      TRS:
167.21/42.78	       b(a(a(x1))) -> a(a(c(a(c(x1)))))
167.21/42.78	       c(a(x1)) -> a(b(x1))
167.21/42.78	     Restore Modifier:
167.21/42.78	      DPs:
167.21/42.78	       c#(a(x1)) -> b#(x1)
167.21/42.78	      TRS:
167.21/42.78	       b(a(a(x1))) -> a(a(c(a(c(x1)))))
167.21/42.78	       c(a(x1)) -> a(b(x1))
167.21/42.78	      EDG Processor:
167.21/42.78	       DPs:
167.21/42.78	        c#(a(x1)) -> b#(x1)
167.21/42.78	       TRS:
167.21/42.78	        b(a(a(x1))) -> a(a(c(a(c(x1)))))
167.21/42.78	        c(a(x1)) -> a(b(x1))
167.21/42.78	       graph:
167.21/42.78	        
167.21/42.78	       SCC Processor:
167.21/42.78	        #sccs: 0
167.21/42.78	        #rules: 0
167.21/42.78	        #arcs: 0/1
167.21/42.78	        
167.21/42.79	EOF