YES

TRS:

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

max/plus interpretations on N:

  a_A(x1) = max{2, 1 + x1}
  a#_A(x1) = max{2, 3}
  b_A(x1) = max{4, 2 + x1}
  b#_A(x1) = max{0, 1}
  c_A(x1) = max{0, -1 + x1}
  c#_A(x1) = max{0, x1}

precedence:

  a = c > b