YES

TRS:

  a(a(x)) -> a(b(a(x)))

max/plus interpretations on N:

  a_A(x1) = max{2, 3}
  a#_A(x1) = max{1, 2 + x1}
  b_A(x1) = max{1, 1}
  b#_A(x1) = max{0, 0}

precedence:

  a > b