Summary: Deciding Inductive Validity of Equations ###
J˜urgen Giesl 1 and Deepak Kapur 2
1 LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
2 Computer Science Dept., University of New Mexico, Albuquerque, NM 87131, USA
Abstract. Kapur and Subramaniam  defined syntactical classes of
equations where inductive validity can be decided automatically. How
ever, these classes are quite restrictive, since defined function symbols
with recursive definitions may only appear on one side of the equations.
In this paper, we expand the decidable class of equations significantly by
allowing both sides of equations to be expressed using defined function
symbols. The definitions of these function symbols must satisfy certain
restrictions which can be checked mechanically. These results are crucial
to increase the applicability of decision procedures for induction.
Mechanized induction often requires user interaction and is incomplete (provers
fail for many valid conjectures). This is especially daunting to an application
expert trying to use an induction prover in cases when conjectures are simple.
Recently, there has been a surge of interest in the role of decision procedures