YES

Problem:
 a(c(d(x))) -> c(x)
 u(b(d(d(x)))) -> b(x)
 v(a(a(x))) -> u(v(x))
 v(a(c(x))) -> u(b(d(x)))
 v(c(x)) -> b(x)
 w(a(a(x))) -> u(w(x))
 w(a(c(x))) -> u(b(d(x)))
 w(c(x)) -> b(x)

Proof:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [w](x0) = x0,
   
   [v](x0) = x0,
   
   [u](x0) = x0,
   
   [b](x0) = x0,
   
   [a](x0) = x0,
   
   [c](x0) = 9x0,
   
   [d](x0) = 2x0
  orientation:
   a(c(d(x))) = 11x >= 9x = c(x)
   
   u(b(d(d(x)))) = 4x >= x = b(x)
   
   v(a(a(x))) = x >= x = u(v(x))
   
   v(a(c(x))) = 9x >= 2x = u(b(d(x)))
   
   v(c(x)) = 9x >= x = b(x)
   
   w(a(a(x))) = x >= x = u(w(x))
   
   w(a(c(x))) = 9x >= 2x = u(b(d(x)))
   
   w(c(x)) = 9x >= x = b(x)
  problem:
   v(a(a(x))) -> u(v(x))
   w(a(a(x))) -> u(w(x))
  Arctic Interpretation Processor:
   dimension: 2
   interpretation:
              [0 1]  
    [w](x0) = [0 0]x0,
    
              [0  0 ]  
    [v](x0) = [-& 0 ]x0,
    
              [0 0]  
    [u](x0) = [0 0]x0,
    
              [1  -&]  
    [a](x0) = [1  2 ]x0
   orientation:
                 [3 4]     [0 0]           
    v(a(a(x))) = [3 4]x >= [0 0]x = u(v(x))
    
                 [4 5]     [0 1]           
    w(a(a(x))) = [3 4]x >= [0 1]x = u(w(x))
   problem:
    
   Qed