  We present a new kind of nontermination argument for linear lasso programs,
called geometric nontermination argument. A geometric nontermination argument
is a finite representation of an infinite execution of the form $(\vec{x} +
\sum_{i=0}^t \lambda^i \vec{y})_{t \geq 0}$. The existence of this
nontermination argument can be stated as a set of nonlinear algebraic
constraints. We show that every linear loop program that has a bounded infinite
execution also has a geometric nontermination argument. Furthermore, we discuss
nonterminating programs that do not have a geometric nontermination argument.
