YES

TRS:

  f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))

linear polynomial interpretations on N:

  f_A(x1) = x1
  f#_A(x1) = x1
  g_A(x1,x2) = x1 + x2
  g#_A(x1,x2) = x1 + x2
  a_A = 0
  a#_A = 0
  h_A(x1,x2) = x1 + x2
  h#_A(x1,x2) = x1 + x2

precedence:

  g > a > h > f