YES

TRS:

  app(app(plus(),0()),y) -> y
  app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
  app(app(app(curry(),f),x),y) -> app(app(f,x),y)
  add() -> app(curry(),plus())

linear polynomial interpretations on N:

  app_A(x1,x2) = x1 + x2 + 2
  app#_A(x1,x2) = x1 + x2 + 2
  plus_A = 2
  plus#_A = 2
  0_A = 1
  0#_A = 1
  s_A = 1
  s#_A = 1
  curry_A = 1
  curry#_A = 1
  add_A = 6
  add#_A = 6

precedence:

  add > app = 0 = curry > plus > s