YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  h > g > a > f = b = i