MAYBE

Problem:
 strict:
  top(left(car(x,y),car(old(),z))) -> top(right(y,car(old(),z)))
  top(left(car(x,car(old(),y)),z)) -> top(right(car(old(),y),z))
  top(right(x,car(y,car(old(),z)))) -> top(left(x,car(old(),z)))
  top(right(car(old(),x),car(y,z))) -> top(left(car(old(),x),z))
  top(left(bot(),car(old(),x))) -> top(right(bot(),car(old(),x)))
  top(right(car(old(),x),bot())) -> top(left(car(old(),x),bot()))
 weak:
  top(left(car(x,y),z)) -> top(left(y,z))
  top(right(x,car(y,z))) -> top(right(x,z))
  bot() -> car(new(),bot())

Proof:
 Open