python

def gen_der(productions,start_symbol,max_derivations=10):
    derivations=[start_symbol]
    for i in range(max_derivations):
        next_derivation=""
        for symbol in derivations[-1]:
            for production in productions:
                lhs,rhs=production.split("->")
                if symbol==lhs:
                    next_derivation+=rhs
        if next_derivation=="":
            break
        derivations.append(next_derivation)
        return derivations
    production=[
        "S->aSb",
        "S->ab",
        ]
    start_symbol="S"
    print(gen_der(productions,start_symbol))