5.62/1.82	YES
5.62/1.82	
5.62/1.82	Problem:
5.62/1.82	 a(a(d(d(x1)))) -> d(d(b(b(x1))))
5.62/1.82	 a(a(x1)) -> b(b(b(b(b(b(x1))))))
5.62/1.82	 b(b(d(d(b(b(x1)))))) -> a(a(c(c(x1))))
5.62/1.82	 c(c(x1)) -> d(d(x1))
5.62/1.82	
5.62/1.82	Proof:
5.62/1.82	 Matrix Interpretation Processor: dim=1
5.62/1.82	  
5.62/1.82	  interpretation:
5.62/1.82	   [c](x0) = 2x0,
5.62/1.82	   
5.62/1.82	   [b](x0) = x0 + 1,
5.62/1.82	   
5.62/1.82	   [a](x0) = x0 + 5,
5.62/1.82	   
5.62/1.82	   [d](x0) = 2x0
5.62/1.82	  orientation:
5.62/1.82	   a(a(d(d(x1)))) = 4x1 + 10 >= 4x1 + 8 = d(d(b(b(x1))))
5.62/1.82	   
5.62/1.82	   a(a(x1)) = x1 + 10 >= x1 + 6 = b(b(b(b(b(b(x1))))))
5.62/1.82	   
5.62/1.82	   b(b(d(d(b(b(x1)))))) = 4x1 + 10 >= 4x1 + 10 = a(a(c(c(x1))))
5.62/1.82	   
5.62/1.82	   c(c(x1)) = 4x1 >= 4x1 = d(d(x1))
5.62/1.82	  problem:
5.62/1.82	   b(b(d(d(b(b(x1)))))) -> a(a(c(c(x1))))
5.62/1.82	   c(c(x1)) -> d(d(x1))
5.62/1.82	  KBO Processor:
5.62/1.82	   weight function:
5.62/1.82	    w0 = 1
5.62/1.82	    w(c) = w(b) = w(d) = 1
5.62/1.82	    w(a) = 0
5.62/1.82	   precedence:
5.62/1.82	    a > c > b ~ d
5.62/1.82	   problem:
5.62/1.82	    
5.62/1.82	   Qed
5.62/1.82	EOF