YES

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

Proof:
 DP Processor:
  DPs:
   d#(u(x)) -> c#(x)
   c#(u(x)) -> b#(x)
  TRS:
   d(x) -> e(u(x))
   d(u(x)) -> c(x)
   c(u(x)) -> b(x)
   v(e(x)) -> x
   b(u(x)) -> a(e(x))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [b#](x0) = -16x0 + 0,
    
    [c#](x0) = -8x0 + 1,
    
    [d#](x0) = 1x0 + 8,
    
    [a](x0) = x0,
    
    [v](x0) = x0 + 0,
    
    [b](x0) = 6x0 + -5,
    
    [c](x0) = 12x0 + 15,
    
    [e](x0) = 1x0 + -2,
    
    [u](x0) = -2x0 + 1,
    
    [d](x0) = 15x0 + 3
   orientation:
    d#(u(x)) = -1x + 8 >= -8x + 1 = c#(x)
    
    c#(u(x)) = -10x + 1 >= -16x + 0 = b#(x)
    
    d(x) = 15x + 3 >= -1x + 2 = e(u(x))
    
    d(u(x)) = 13x + 16 >= 12x + 15 = c(x)
    
    c(u(x)) = 10x + 15 >= 6x + -5 = b(x)
    
    v(e(x)) = 1x + 0 >= x = x
    
    b(u(x)) = 4x + 7 >= 1x + -2 = a(e(x))
   problem:
    DPs:
     
    TRS:
     d(x) -> e(u(x))
     d(u(x)) -> c(x)
     c(u(x)) -> b(x)
     v(e(x)) -> x
     b(u(x)) -> a(e(x))
   Qed