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))

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2
  +#_A(x1,x2) = 1
  a_A = 0
  a#_A = 3
  b_A = 0
  b#_A = 0
  f_A(x1,x2) = 0
  f#_A(x1,x2) = x1 + x2 + 2

precedence:

  f > + > a > b