NO

Problem:
 strict:
  -(x,0()) -> x
  -(s(x),s(y)) -> -(x,y)
  quot(0(),s(y)) -> 0()
  quot(s(x),s(y)) -> s(quot(-(x,y),s(y)))
 weak:
  gen() -> 0()
  gen() -> s(gen())

Proof:
 Unfolding Processor:
  loop length: 3
  terms:
   quot(gen(),s(0()))
   quot(s(gen()),s(0()))
   s(quot(-(gen(),0()),s(0())))
  context: s([])
  substitution:
   
  Qed