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Summary: Automated Termination Analysis of java bytecode
by Term Rewriting
J¨urgen Giesl
LuFG Informatik 2, RWTH Aachen University, Germany
joint work with C. Otto, M. Brockschmidt, C. von Essen
Termination Analysis for TRSs
R : plus(x, 0) x
plus(x, s(y)) s(plus(x, y))
R is terminating iff there is no infinite evaluation t1 R t2 R . . .
Computation of "2 + 1": plus(s(s(0)), s(0)) R s(plus(s(s(0)), 0))
R s(s(s(0)))
easier / more general than for programs
suitable for automation
But: halting problem is undecidable!
automated termination proofs do not always succeed
Termination Analysis for TRSs
Pol( plus(0, y) ) > Pol( y )
Pol( plus(s(x), y) ) > Pol( s(plus(x, y)) )
R is terminating iff there is no infinite evaluation t1 R t2 R . . .
Goal: Find order such that r for all rules r R
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