YES

TRS:

  minus(minus(x)) -> x
  minux(+(x,y)) -> +(minus(y),minus(x))
  +(minus(x),+(x,y)) -> y
  +(+(x,y),minus(y)) -> x

max/plus interpretations on N:

  minus_A(x1) = max{0, x1}
  minus#_A(x1) = max{0, x1}
  minux_A(x1) = max{0, x1}
  minux#_A(x1) = max{0, x1}
  +_A(x1,x2) = max{0, x1, x2}
  +#_A(x1,x2) = max{0, x1, x2}

precedence:

  minux = + > minus