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Summary: Deciding Innermost Loops
Ren´e Thiemann1
, J¨urgen Giesl2
, and Peter Schneider-Kamp2
1
Institute of Computer Science, University of Innsbruck, Austria
rene.thiemann@uibk.ac.at
2
LuFG Informatik 2, RWTH Aachen University, Germany
{giesl,psk}@informatik.rwth-aachen.de
Abstract. We present the first method to disprove innermost termina-
tion of term rewrite systems automatically. To this end, we first develop
a suitable notion of an innermost loop. Second, we show how to detect in-
nermost loops: One can start with any technique amenable to find loops.
Then our novel procedure can be applied to decide whether a given loop
is an innermost loop. We implemented and successfully evaluated our
method in the termination prover AProVE.
1 Introduction
Termination is an important property of term rewrite systems (TRSs). Therefore,
much effort has been spent on developing and automating powerful techniques
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