| Тойм: | We present a new method for the constraint-based synthesis of termination
arguments for linear loop programs based on linear ranking templates. Linear
ranking templates are parameterized, well-founded relations such that an
assignment to the parameters gives rise to a ranking function. Our approach
generalizes existing methods and enables us to use templates for many different
ranking functions with affine-linear components. We discuss templates for
multiphase, nested, piecewise, parallel, and lexicographic ranking functions.
These ranking templates can be combined to form more powerful templates.
Because these ranking templates require both strict and non-strict
inequalities, we use Motzkin's transposition theorem instead of Farkas' lemma
to transform the generated $\exists\forall$-constraint into an
$\exists$-constraint.
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