YES

TRS:

  minus(x,0()) -> x
  minus(s(x),s(y)) -> minus(x,y)
  quot(0(),s(y)) -> 0()
  quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
  plus(0(),y) -> y
  plus(s(x),y) -> s(plus(x,y))
  minus(minus(x,y),z) -> minus(x,plus(y,z))
  app(nil(),k) -> k
  app(l,nil()) -> l
  app(cons(x,l),k) -> cons(x,app(l,k))
  sum(cons(x,nil())) -> cons(x,nil())
  sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
  sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))

linear polynomial interpretations on N:

  minus_A(x1,x2) = x1
  minus#_A(x1,x2) = 2
  0_A = 1
  0#_A = 1
  s_A(x1) = x1 + 1
  s#_A(x1) = 0
  quot_A(x1,x2) = x1 + x2
  quot#_A(x1,x2) = x1 + x2 + 1
  plus_A(x1,x2) = x1 + x2 + 1
  plus#_A(x1,x2) = 1
  app_A(x1,x2) = x1 + x2 + 1
  app#_A(x1,x2) = 7
  nil_A = 1
  nil#_A = 4
  cons_A(x1,x2) = x2 + 4
  cons#_A(x1,x2) = 6
  sum_A(x1) = 5
  sum#_A(x1) = x1

precedence:

  quot = nil > minus = sum > 0 = plus = app > s = cons