4.82/1.74	YES
4.82/1.74	
4.82/1.74	Problem:
4.82/1.74	 a(a(x1)) -> b(b(b(x1)))
4.82/1.74	 b(x1) -> c(c(d(x1)))
4.82/1.74	 c(x1) -> d(d(d(x1)))
4.82/1.74	 b(c(x1)) -> c(b(x1))
4.82/1.74	 b(c(d(x1))) -> a(x1)
4.82/1.74	
4.82/1.74	Proof:
4.82/1.74	 String Reversal Processor:
4.82/1.74	  a(a(x1)) -> b(b(b(x1)))
4.82/1.74	  b(x1) -> d(c(c(x1)))
4.82/1.74	  c(x1) -> d(d(d(x1)))
4.82/1.74	  c(b(x1)) -> b(c(x1))
4.82/1.74	  d(c(b(x1))) -> a(x1)
4.82/1.74	  Matrix Interpretation Processor: dim=1
4.82/1.74	   
4.82/1.74	   interpretation:
4.82/1.74	    [c](x0) = x0 + 4,
4.82/1.74	    
4.82/1.74	    [d](x0) = x0,
4.82/1.74	    
4.82/1.74	    [b](x0) = x0 + 8,
4.82/1.74	    
4.82/1.74	    [a](x0) = x0 + 12
4.82/1.74	   orientation:
4.82/1.74	    a(a(x1)) = x1 + 24 >= x1 + 24 = b(b(b(x1)))
4.82/1.74	    
4.82/1.74	    b(x1) = x1 + 8 >= x1 + 8 = d(c(c(x1)))
4.82/1.74	    
4.82/1.74	    c(x1) = x1 + 4 >= x1 = d(d(d(x1)))
4.82/1.74	    
4.82/1.74	    c(b(x1)) = x1 + 12 >= x1 + 12 = b(c(x1))
4.82/1.74	    
4.82/1.74	    d(c(b(x1))) = x1 + 12 >= x1 + 12 = a(x1)
4.82/1.74	   problem:
4.82/1.74	    a(a(x1)) -> b(b(b(x1)))
4.82/1.74	    b(x1) -> d(c(c(x1)))
4.82/1.74	    c(b(x1)) -> b(c(x1))
4.82/1.74	    d(c(b(x1))) -> a(x1)
4.82/1.74	   Matrix Interpretation Processor: dim=1
4.82/1.74	    
4.82/1.74	    interpretation:
4.82/1.74	     [c](x0) = x0,
4.82/1.74	     
4.82/1.74	     [d](x0) = x0 + 1,
4.82/1.74	     
4.82/1.74	     [b](x0) = x0 + 1,
4.82/1.74	     
4.82/1.74	     [a](x0) = x0 + 2
4.82/1.74	    orientation:
4.82/1.74	     a(a(x1)) = x1 + 4 >= x1 + 3 = b(b(b(x1)))
4.82/1.75	     
4.82/1.75	     b(x1) = x1 + 1 >= x1 + 1 = d(c(c(x1)))
4.82/1.75	     
4.82/1.75	     c(b(x1)) = x1 + 1 >= x1 + 1 = b(c(x1))
4.82/1.75	     
4.82/1.75	     d(c(b(x1))) = x1 + 2 >= x1 + 2 = a(x1)
4.82/1.75	    problem:
4.82/1.75	     b(x1) -> d(c(c(x1)))
4.82/1.75	     c(b(x1)) -> b(c(x1))
4.82/1.75	     d(c(b(x1))) -> a(x1)
4.82/1.75	    KBO Processor:
4.82/1.75	     weight function:
4.82/1.75	      w0 = 1
4.82/1.75	      w(d) = w(b) = w(a) = 1
4.82/1.75	      w(c) = 0
4.82/1.75	     precedence:
4.82/1.75	      c > b > d ~ a
4.82/1.75	     problem:
4.82/1.75	      
4.82/1.75	     Qed
4.82/1.75	EOF