Generation of Inverse Term Rewriting Systems for Pure Treeless Functions

In this paper, we present how to construct an inverse term rewriting system that implements the inverses of in a pure treeless TRS. At the first step, we propose an algorithm for generating a conditional TRS that computes the inverses of pure treeless functions. We prove that the conditional TRS constructed by our algorithm implements the inverses of those functions defined by a given pure treeless TRS. Next, we show that the conditional TRS generated by our algorithm can be transformed to an equivalent TRS. Moreover, if the input pure treeless TRS of the algorithm is right-linear then the resulting TRS is left-linear.