YES

TRS:

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

linear polynomial interpretations on N:

  minus_A(x1) = x1
  minus#_A(x1) = x1
  minux_A(x1) = x1 + 1
  minux#_A(x1) = x1 + 1
  +_A(x1,x2) = x1 + x2 + 1
  +#_A(x1,x2) = x1 + x2 + 1

precedence:

  minux > + > minus