6.96/2.20	YES
7.31/2.20	
7.31/2.20	Problem:
7.31/2.20	 b(c(a(x1))) -> a(b(x1))
7.31/2.20	 b(b(b(x1))) -> c(a(c(x1)))
7.31/2.20	 c(d(x1)) -> d(c(x1))
7.31/2.20	 c(d(b(x1))) -> d(c(c(x1)))
7.31/2.20	 d(c(x1)) -> b(b(b(x1)))
7.31/2.20	 c(b(x1)) -> d(a(x1))
7.31/2.20	 d(b(c(x1))) -> a(a(x1))
7.31/2.20	 d(a(x1)) -> b(x1)
7.31/2.20	
7.31/2.20	Proof:
7.31/2.20	 String Reversal Processor:
7.31/2.20	  a(c(b(x1))) -> b(a(x1))
7.31/2.20	  b(b(b(x1))) -> c(a(c(x1)))
7.31/2.20	  d(c(x1)) -> c(d(x1))
7.31/2.20	  b(d(c(x1))) -> c(c(d(x1)))
7.31/2.20	  c(d(x1)) -> b(b(b(x1)))
7.31/2.20	  b(c(x1)) -> a(d(x1))
7.31/2.20	  c(b(d(x1))) -> a(a(x1))
7.31/2.20	  a(d(x1)) -> b(x1)
7.31/2.20	  Matrix Interpretation Processor: dim=1
7.31/2.20	   
7.31/2.20	   interpretation:
7.31/2.20	    [d](x0) = x0 + 2,
7.31/2.20	    
7.31/2.20	    [b](x0) = x0 + 1,
7.31/2.20	    
7.31/2.20	    [c](x0) = x0 + 1,
7.31/2.20	    
7.31/2.20	    [a](x0) = x0
7.31/2.20	   orientation:
7.31/2.20	    a(c(b(x1))) = x1 + 2 >= x1 + 1 = b(a(x1))
7.31/2.20	    
7.31/2.20	    b(b(b(x1))) = x1 + 3 >= x1 + 2 = c(a(c(x1)))
7.31/2.20	    
7.31/2.20	    d(c(x1)) = x1 + 3 >= x1 + 3 = c(d(x1))
7.31/2.20	    
7.31/2.20	    b(d(c(x1))) = x1 + 4 >= x1 + 4 = c(c(d(x1)))
7.31/2.20	    
7.31/2.20	    c(d(x1)) = x1 + 3 >= x1 + 3 = b(b(b(x1)))
7.31/2.20	    
7.31/2.20	    b(c(x1)) = x1 + 2 >= x1 + 2 = a(d(x1))
7.31/2.20	    
7.31/2.20	    c(b(d(x1))) = x1 + 4 >= x1 = a(a(x1))
7.31/2.20	    
7.31/2.20	    a(d(x1)) = x1 + 2 >= x1 + 1 = b(x1)
7.31/2.20	   problem:
7.31/2.20	    d(c(x1)) -> c(d(x1))
7.31/2.20	    b(d(c(x1))) -> c(c(d(x1)))
7.31/2.20	    c(d(x1)) -> b(b(b(x1)))
7.31/2.20	    b(c(x1)) -> a(d(x1))
7.31/2.20	   Matrix Interpretation Processor: dim=1
7.31/2.20	    
7.31/2.20	    interpretation:
7.31/2.20	     [d](x0) = 4x0,
7.31/2.20	     
7.31/2.20	     [b](x0) = 2x0,
7.31/2.20	     
7.31/2.20	     [c](x0) = 2x0 + 1,
7.31/2.20	     
7.31/2.20	     [a](x0) = x0 + 2
7.31/2.20	    orientation:
7.31/2.20	     d(c(x1)) = 8x1 + 4 >= 8x1 + 1 = c(d(x1))
7.31/2.20	     
7.31/2.20	     b(d(c(x1))) = 16x1 + 8 >= 16x1 + 3 = c(c(d(x1)))
7.31/2.20	     
7.31/2.20	     c(d(x1)) = 8x1 + 1 >= 8x1 = b(b(b(x1)))
7.31/2.20	     
7.31/2.20	     b(c(x1)) = 4x1 + 2 >= 4x1 + 2 = a(d(x1))
7.31/2.20	    problem:
7.31/2.20	     b(c(x1)) -> a(d(x1))
7.31/2.20	    String Reversal Processor:
7.31/2.20	     c(b(x1)) -> d(a(x1))
7.31/2.20	     KBO Processor:
7.31/2.20	      weight function:
7.31/2.20	       w0 = 1
7.31/2.20	       w(b) = w(c) = w(a) = 1
7.31/2.20	       w(d) = 0
7.31/2.20	      precedence:
7.31/2.20	       d > b ~ c ~ a
7.31/2.20	      problem:
7.31/2.20	       
7.31/2.20	      Qed
7.31/2.20	EOF