YES

TRS:

  f(a()) -> g(h(a()))
  h(g(x)) -> g(h(f(x)))
  k(x,h(x),a()) -> h(x)
  k(f(x),y,x) -> f(x)

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = x1
  a_A = 5
  a#_A = 0
  g_A(x1) = 2
  g#_A(x1) = x1 + 1
  h_A(x1) = 2
  h#_A(x1) = 4
  k_A(x1,x2,x3) = x1 + x3
  k#_A(x1,x2,x3) = x1 + 5

precedence:

  k > h > g > f > a