Summary: Deciding Innermost Loops
, J¨urgen Giesl2
, and Peter Schneider-Kamp2
Institute of Computer Science, University of Innsbruck, Austria
LuFG Informatik 2, RWTH Aachen University, Germany
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.
Termination is an important property of term rewrite systems (TRSs). Therefore,
much effort has been spent on developing and automating powerful techniques