# Finite Transition Models, Halt Truncation, and Stuck States

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261013-advance-20261019-r04-computational-model-foundations · 2026-10-13 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0001/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 2. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5]], [0, 1, 2, 3, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5]], [0, 1, 2, 3, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0002/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 3. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0003/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 4. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0004/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 5. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0005/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 6. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0006/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 7. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0007/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 8. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0008/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 9. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0009/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 10. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0010/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 11. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0011/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 12. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0012/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 13. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0013/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 14. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0014/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 15. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0015/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 16. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0016/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 17. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0017/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 18. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0018/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 19. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0019/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 20. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0020/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 21. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0021/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 22. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0022/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 23. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0023/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 24. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0024/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 25. Complete Reachability with Halt Outgoing Edges Truncated

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.

View answer and explanation(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])

Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0025/)

Abstract computational model · qf-ext19-model-reachable-states · candidate





## 26. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0026/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 27. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0027/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 28. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0028/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 29. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 6], [Yes, No], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0029/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 30. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0030/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 31. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0031/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 32. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0032/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 33. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 6], [Yes, No], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0033/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 34. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0034/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 35. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0035/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 36. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0036/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 37. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 6], [Yes, No], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0037/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 38. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0038/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 39. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0039/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 40. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0040/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 41. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 6], [Yes, No], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0041/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 42. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0042/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 43. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0043/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 44. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0044/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 45. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 6], [Yes, No], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0045/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 46. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0046/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 47. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0047/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 48. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0048/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 49. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 6], [Yes, No], Yes, Yes, [No], No, No)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0049/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 50. Legal Finite Trace Prefix and Post-Halt Continuation Guard

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.

View answer and explanation([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)

Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0050/)

Abstract computational model · qf-ext19-model-trace-qualification · candidate





## 51. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0051/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 52. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0052/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 53. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0053/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 54. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0054/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 55. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0055/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 56. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0056/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 57. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0057/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 58. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0058/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 59. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0059/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 60. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0060/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 61. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0061/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 62. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0062/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 63. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0063/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 64. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0064/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 65. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0065/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 66. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0066/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 67. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0067/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 68. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0068/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 69. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0069/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 70. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0070/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 71. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0071/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 72. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0072/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 73. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0073/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 74. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0074/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 75. Reachable Halt, Stuck, and Active States

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).

View answer and explanation([0, 1, 2, 5], [5], [], [0, 1, 2])

A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0075/)

Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate





## 76. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0076/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 77. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0077/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 78. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0078/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 79. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 4, 5], [4], No, No, reachable stuck-nonhalting-state)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], No, No, reachable stuck-nonhalting-state).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0079/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 80. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0080/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 81. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0081/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 82. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0082/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 83. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 4, 5], [], No, Yes, all-finite-model-paths-reach-halt)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], No, Yes, all-finite-model-paths-reach-halt).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0083/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 84. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0084/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 85. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0085/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 86. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0086/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 87. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0087/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 88. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0088/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 89. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0089/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 90. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0090/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 91. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0091/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 92. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0092/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 93. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0093/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 94. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0094/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 95. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0095/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 96. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0096/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 97. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0097/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 98. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0098/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 99. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0099/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate





## 100. All-Path Finite Termination and Reachable Nonhalting Cycles

Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.

View answer and explanation([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)

Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261019-r04-computational-model-0100/)

Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261019-r04-computational-model-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261019-r04-computational-model-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261019-r04-computational-model-foundations/validation-report.json)