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§1.2, The CSP View of the World defines CSP events, CSP hiding, CSP refinement and the supported CSP semantic models. This source is cited for the meanings of the models, not for answers to the 2015 examination.

The obstruction is that the property is about where a transition originates, whereas the three standard CSP semantic models identify processes that can disagree about this fact. Take fresh $h\ne a$ and compareIn $G$, the only $a$ transition leaves a CSP stable state, so the property holds. Initially $B$ has both an $a$ transition to $\mathrm{STOP}$ and a CSP internal action to $a\to \mathrm{STOP}$. Its initial state is therefore not a CSP stable state, and its direct $a$ transition violates the property.

Nevertheless both have exactly the CSP traces $⟨⟩$ and $⟨a⟩$. Initially their possible stable observations offer exactly $a$, so their initial CSP stable failures are precisely $(⟨⟩,X)$ with $a\notin X$. After $a$, both can refuse every CSP event. Neither has a CSP divergence: the hidden $h$ can occur at most once. ThereforeNo CSP refinement test in one of these models can separate semantically equal operands. This also rules out placing the operand in a fixed context of ordinary CSP operators before the test, since those operators respect the model's equality. A model recording more about the interleaving of stability and acceptance, or an additional operator that explicitly observes stability, would be needed.

This is a safety property: a bad shutdown or a later reactivation has a finite bad CSP trace. Use the CSP traces model. Let $V=\{0,\dots ,N-1\}$, let $A\subseteq V$ track active nodes, and let $D\subseteq V$ track nodes that have announced shutdown. Let $\mathrm{Ring}$ contain every message CSP event. Define the following specification over the status-signal alphabet:Use the CSP refinement checkThe specification offers a shutdown only if the active set is empty, and offers no activation once $D$ is nonempty. A trace violating either requirement is therefore absent from the specification. Recording $D$ also prevents duplicate shutdowns and any status change by an already shut-down node. CSP hiding removes message details irrelevant to this finite bad-prefix check; a CSP traces model check alone does not assert eventual progress.

The system satisfies the check. After the first message has passed nodes $1,\dots ,i$, its bit is the Boolean conjunction of their being idle when sampled. Every sampled node is then frozen until it forwards the second-round decision. A true bit returning to node $0$ therefore means that every non-coordinator is idle and still frozen; the coordinator has itself remained idle. A true decision consequently reaches only idle nodes, each of which proceeds to shutdown rather than returning to $\mathrm{Free}$. No node can subsequently become active. A false decision permits no shutdown at all.

The trigger is specifically the first-round reception $ring.0.\mathrm{true}$. A CSP trace restriction cannot by itself guarantee progress after this event, because a finite prefix is compatible with both completion and an indefinitely delayed completion. We need to exclude both a stable refusal to continue and CSP divergence, so use the CSP failures-divergences model.

Here is an explicit conditional check that imposes no progress requirement before the trigger. Build the reachable labelled transition system of $\mathrm{System}$ and observe coordinator rounds with a two-phase monitor: it starts in the first-return phase and toggles on each $ring.0.b$. Collect the set $\mathcal{H}$ of system derivatives immediately after a true return in the first-return phase. This distinguishes the survey's return from the decision's return, without changing any system transitions. For fixed finite $N$, the set is finite. DefineHere $\sqcap$ denotes CSP internal choice. Perform the single CSP refinement checkEquivalently, check each post-trigger derivative $H$ individually against $\mathrm{Finish}(\varnothing )$ after the displayed CSP hiding. If the trigger is unreachable, the conditional property is vacuously true and there is no post-trigger check to perform.

The CSP internal choice in $\mathrm{Finish}$ deliberately permits any next shutdown, including an implementation that offers only one of the remaining shutdowns. It forbids a stable refusal of all remaining shutdowns, has no CSP divergence, and permits at most $N$ distinct shutdowns before $\mathrm{STOP}$. A CSP external choice over all remaining nodes would instead demand simultaneous readiness for every remaining shutdown and would unnecessarily reject the protocol's sequential delivery.

After hiding all other actions, endless internal work becomes a CSP divergence and a blocked unfinished state becomes a forbidden CSP stable failure. Since there are only $N$ possible shutdown actions and duplicates are excluded by CSP traces, every maximal progressing execution must complete all $N$. As usual for untimed CSP, this progress claim assumes the environment allows shutdown signals to occur; it supplies no wall-clock deadline. No fairness assumption requiring the coordinator eventually to initiate a survey has been smuggled into this conditional check.

For the defined system the check succeeds. Immediately after the trigger all statuses are idle and frozen. The only message work left is the second round: node $0$ sends the decision to node $1$, nodes $1$ through $N-1$ forward it, and node $0$ receives it. These are exactly $N$ more message transfers. Each node then has its one shutdown action, and the message can advance even while an earlier node's shutdown is pending. Thus there are no remaining status changes, no message cycle, and no unfinished global state in which every action is blocked. The measurestarts at $2N$, is nonnegative, and decreases on every subsequent transition. This excludes any hidden infinite run; before all shutdowns finish there is either an enabled message transfer or an enabled shutdown signal. The operational argument proves the conditional claim for every $N\ge 2$; finite state enumeration is only a supporting check.