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Isabel Oitavem has introduced a term rewriting system (TRS) which captures the class FPS of polynomial-space computable functions. We propose an alternative TRS for FPS. As a consequence, it is obtained that FPS is the smallest class containing certain initial functions and closed under specific operations. It turns out that our characterization is(More)
We propose a new order, the small polynomial path order (sPOP * for short). The order sPOP * provides a characterisation of the class of polynomial time computable function via term rewrite systems. Any polynomial time computable function gives rise to a rewrite system that is compatible with sPOP *. On the other hand any function defined by a rewrite(More)
In this paper we present a new path order for rewrite systems, the exponential path order EPO. Suppose a term rewrite system is compatible with EPO , then the runtime complexity of this rewrite system is bounded from above by an exponential function. Furthermore, the class of function computed by a rewrite system compatible with EPO equals the class of(More)
The predicative lexicographic path order (PLPO for short), a syntactic restriction of the lex-icographic path order, is presented. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recursion with parameter substitution, unnested multiple recursion, or simple nested recursion, can be oriented with PLPOs.(More)
In this paper we present a novel termination order the pred-icative lexicographic path order (PLPO for short), a syntactic restriction of the lexicographic path order. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recur-sion with parameter substitution, unnested multiple recursion, or simple nested(More)
In this paper we present a new path order for rewrite systems, the exponential path order EPO ⋆. Suppose a term rewrite system R is compatible with EPO ⋆ , then the runtime complexity of R is bounded from above by an exponential function. Further, the class of function computed by a rewrite system compatible with EPO ⋆ equals the class of functions(More)