YES

TRS:

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

max/plus interpretations on N:

  a_A(x1) = max{12, 23 + x1}
  a#_A(x1) = max{23, -10 + x1}
  b_A(x1) = max{4, 7 + x1}
  b#_A(x1) = max{0, -1 + x1}

precedence:

  a > b