YES

TRS:

  +(a(),b()) -> +(b(),a())
  +(a(),+(b(),z)) -> +(b(),+(a(),z))
  +(+(x,y),z) -> +(x,+(y,z))
  f(a(),y) -> a()
  f(b(),y) -> b()
  f(+(x,y),z) -> +(f(x,z),f(y,z))

max/plus interpretations on N:

  +_A(x1,x2) = max{2, x1, x2}
  +#_A(x1,x2) = max{2, x1, x2}
  a_A = 3
  a#_A = 3
  b_A = 1
  b#_A = 1
  f_A(x1,x2) = max{4, 1 + x1, 4 + x2}
  f#_A(x1,x2) = max{4, 1 + x1, 4 + x2}

precedence:

  a > b > f > +