#### keywords

Term Rewriting, Complexity, Proof Theory, and Logic.

#### term rewriting

Term rewriting is a conceptual simple, but powerful abstract model of computation. The foundation of rewriting is equational logic and TRSs are conceivable as sets of directed equations. In order to assess the complexity of a TRS it is natural to look at the maximal length of derivation sequences. This viewpoint gives rise to the study of the complexity of TRSs, a topic that lies at the heart of my research interests. This work seems applicable in automated complexity analysis of programs and current work is dedicated towards such applications.

#### proof theory

Proof theory is one of the central pillars of mathematical logic. Proof-theoretic investigations in Hilbert's tradition were mainly concerned with questions of provability. However, in order to study provability a more refined study of the structure of proofs is needed. This observation led to investigations into structural proof theory. Structural proof theory plays a crucial role in the foundations of programming language. My interest in structural proof theory encompasses Herbrand's Theorem, Hilbert's epsilon calculus, Curry-Howard correspondence and deep inference.