“…A transition system is a tuple S, ∆, sι where S is a (possibly infinite) set of control states, sι ∈ S is the initial control state, and ∆ ⊆ S × S is a set of transitions. A weighted transition system (WTS) is a tuple S = S, ∆, sι, ν where S, ∆, sι is a transition system, and ν : ∆ → Z is a weight function labeling transitions with integer weights 1 . A battery transition system (BTS or battery system, for short) is a tuple B = S, ∆, sι, ν , c, k where S, ∆, sι, ν is a WTS with a finite number of control states (i.e.,…”