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)

max/plus interpretations on N:

  f_A(x1) = max{10, -2}
  f#_A(x1) = max{4, 1 + x1}
  a_A = 6
  a#_A = 5
  g_A(x1) = max{1, -1}
  g#_A(x1) = max{5, 2 + x1}
  h_A(x1) = max{1, -7 + x1}
  h#_A(x1) = max{6, 6}
  k_A(x1,x2,x3) = max{10, -1 + x1, -8, -8}
  k#_A(x1,x2,x3) = max{0, 0, 0, 0}

precedence:

  h > g = k > f > a