The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by innermost rewriting is polynomially bounded. Every unfolding graph rewrite rule is precedence terminating in the sense of Middeldorp, Ohsaki and Zantema. Although precedence terminating infinite rewrite systems cover all the primitive recursive functions, in this paper we consider graph rewrite systems precedence terminating with argument separation, which form a subclass of precedence terminating graph rewrite systems. We show that for any precedence terminating infinite graph rewrite system G with a specific argument separation, both the runtime complexity of G and the size of every normal form in G can be polynomially bounded. As a corollary, we obtain an alternative proof of the original result by Dal Lago et al.

翻译：安全重现( 或放大重现) 的一般形式可以用一个无限的图形重写系统来表示, 包括 Dal Lago、 Martini 和 Zorzi 引入的演示式图形重写规则, 其中, 最内层重写的每种正常形式大小都存在多元的界限。 每一个正在发展中的图形重写规则都是优先的, 都以Middeldorp、 Ohsaki 和 Zantema 的意义上的终止。 虽然终止无限重现系统的优先权涵盖所有原始重现功能, 但本文中我们把图形重现系统放在优先位置上, 终止参数分离, 形成终止图形重写系统的子类。 我们显示, 对于任何终止无限图重写系统的优先, 并具体区分参数 G 的运行时间复杂性和 G 中每种正常形式的大小, 都可以以多元的界限为主。 作为必然结果的替代证据, 由 Dal Lago 等人 等人 提供 。