YES

TRS:

  f(x,y) -> x
  g(a()) -> h(a(),b(),a())
  i(x) -> f(x,x)
  h(x,x,y) -> g(x)

max/plus interpretations on N:

  f_A(x1,x2) = max{0, x1, x2}
  f#_A(x1,x2) = max{0, x1, x2}
  g_A(x1) = max{5, 3 + x1}
  g#_A(x1) = max{5, 3 + x1}
  a_A = 4
  a#_A = 4
  h_A(x1,x2,x3) = max{6, x1, 4 + x2, x3}
  h#_A(x1,x2,x3) = max{6, x1, 4 + x2, x3}
  b_A = 3
  b#_A = 3
  i_A(x1) = max{1, 1 + x1}
  i#_A(x1) = max{1, 1 + x1}

precedence:

  g = i > f = h = b > a