Simple gap termination for term graph rewriting systems

This paper proves the extension of Kruskal-Friedman theorem, which is an extension of the ordinary Kruskal's theorem with gap-condition, on !-trees (Main theorem 1 in section 3). Based on the theorem, a new termination criteria for cyclic term graph rewriting systems, named simple gap termination (Main theorem 2 in section 4), is proposed where the naive extension of simple termination (based on [Lav78]) does not work well.