4.58/1.48	YES
4.58/1.49	
4.58/1.49	Problem:
4.58/1.49	 a(a(x1)) -> b(c(x1))
4.58/1.49	 b(b(x1)) -> c(d(x1))
4.58/1.49	 c(c(x1)) -> d(d(d(x1)))
4.58/1.49	 d(d(d(x1))) -> a(c(x1))
4.58/1.49	
4.58/1.49	Proof:
4.58/1.49	 Matrix Interpretation Processor: dim=1
4.58/1.49	  
4.58/1.49	  interpretation:
4.58/1.49	   [d](x0) = x0 + 6,
4.58/1.49	   
4.58/1.49	   [b](x0) = x0 + 9,
4.58/1.49	   
4.58/1.49	   [c](x0) = x0 + 9,
4.58/1.49	   
4.58/1.49	   [a](x0) = x0 + 9
4.58/1.49	  orientation:
4.58/1.49	   a(a(x1)) = x1 + 18 >= x1 + 18 = b(c(x1))
4.58/1.49	   
4.58/1.49	   b(b(x1)) = x1 + 18 >= x1 + 15 = c(d(x1))
4.58/1.49	   
4.58/1.49	   c(c(x1)) = x1 + 18 >= x1 + 18 = d(d(d(x1)))
4.58/1.49	   
4.58/1.49	   d(d(d(x1))) = x1 + 18 >= x1 + 18 = a(c(x1))
4.58/1.49	  problem:
4.58/1.49	   a(a(x1)) -> b(c(x1))
4.58/1.49	   c(c(x1)) -> d(d(d(x1)))
4.58/1.49	   d(d(d(x1))) -> a(c(x1))
4.58/1.49	  String Reversal Processor:
4.58/1.49	   a(a(x1)) -> c(b(x1))
4.58/1.49	   c(c(x1)) -> d(d(d(x1)))
4.58/1.49	   d(d(d(x1))) -> c(a(x1))
4.58/1.49	   Matrix Interpretation Processor: dim=1
4.58/1.49	    
4.58/1.49	    interpretation:
4.58/1.49	     [d](x0) = x0 + 2,
4.58/1.49	     
4.58/1.49	     [b](x0) = x0 + 1,
4.58/1.49	     
4.58/1.49	     [c](x0) = x0 + 3,
4.58/1.49	     
4.58/1.49	     [a](x0) = x0 + 2
4.58/1.49	    orientation:
4.58/1.49	     a(a(x1)) = x1 + 4 >= x1 + 4 = c(b(x1))
4.58/1.49	     
4.58/1.49	     c(c(x1)) = x1 + 6 >= x1 + 6 = d(d(d(x1)))
4.58/1.49	     
4.58/1.49	     d(d(d(x1))) = x1 + 6 >= x1 + 5 = c(a(x1))
4.58/1.49	    problem:
4.58/1.49	     a(a(x1)) -> c(b(x1))
4.58/1.49	     c(c(x1)) -> d(d(d(x1)))
4.58/1.49	    String Reversal Processor:
4.58/1.49	     a(a(x1)) -> b(c(x1))
4.58/1.49	     c(c(x1)) -> d(d(d(x1)))
4.58/1.49	     KBO Processor:
4.58/1.49	      weight function:
4.58/1.49	       w0 = 1
4.58/1.49	       w(b) = w(c) = w(a) = 1
4.58/1.49	       w(d) = 0
4.58/1.49	      precedence:
4.58/1.49	       d > a > b ~ c
4.58/1.49	      problem:
4.58/1.49	       
4.58/1.49	      Qed
4.58/1.49	EOF