In Abstract geometrical computation for black hole
computation (MCU '04, LNCS 3354), the author
provides a setting based on rational numbers, abstract
geometrical computation, with super-Turing capability.
the present paper, we prove the Turing computing capability
of reversible conservative abstract geometrical computation.
allows backtracking as well as saving energy; it corresponds here to
the local reversibility of collisions.
corresponds to the preservation of some other energy ensuring that the
number of signals remains bounded.
We first consider 2-counter automata enhanced with a stack to keep
track of the computation.
Then we prove that they can be simulated by reversible conservative