# Question 27560: The Complete Bounded Language Includes Epsilon and Terminates Epsilon Cycles [Return to catalogue page 138](https://ocme.evemisslab.com/en/questions/page/138/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261015-advance-20261118-r06-regular-expression-foundations/#q-20261015-advance-20261118-r06-regular-expression-0035) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0054-27560 · q-20261015-advance-20261118-r06-regular-expression-0035 ## Original question and givens Use alphabet=[a, b, c] and typed regular-expression AST={"type":"union","children":[{"type":"concat","children":[{"type":"symbol","value":"a"},{"type":"symbol","value":"b"},{"type":"symbol","value":"c"},{"type":"symbol","value":"a"},{"type":"symbol","value":"b"}]},{"type":"star","child":{"type":"symbol","value":"b"}}]}. Words are arrays of alphabet symbols; distinguish empty language from the language containing the empty word. Enumerate every accepted word of length at most=5. Give (alphabet, canonical_typed_AST, max_length, complete_bounded_language, word_count, bounded_enumeration_complete, epsilon_cycle_scope). - G001 — Use alphabet=[a, b, c] and typed regular-expression AST={"type":"union","children":[{"type":"concat","children":[{"type":"symbol","value":"a"},{"type":"symbol","value":"b"},{"type":"symbol","value":"c"},{"type":"symbol","value":"a"},{"type":"symbol","value":"b"}]},{"type":"star","child":{"type":"symbol","value":"b"}}]}. Words are arrays of alphabet symbols; distinguish empty language from the language containing the empty word. Enumerate every accepted word of length at most=5. Give (alphabet, canonical_typed_AST, max_length, complete_bounded_language, word_count, bounded_enumeration_complete, epsilon_cycle_scope). ## Definition and scope Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate. - [mko-regular-expression](https://ocme.evemisslab.com/en/mko/mko-regular-expression/) ## Step-by-step derivation S001 · impliesBefore source roles = [regex-bounded-language] After derived = [[alphabet, canonical_typed_AST, max_length, complete_bounded_language, word_count, bounded_enumeration_complete, epsilon_cycle_scope]] Conditions: none List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct. Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001 S002 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[0].children[0], [a, b, c], {'type': 'symbol', 'value': 'a'}] After derived = [{'type': 'symbol', 'value': 'a'}, {type:"symbol",value:"a"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S001 S003 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[0].children[1], [a, b, c], {'type': 'symbol', 'value': 'b'}] After derived = [{'type': 'symbol', 'value': 'b'}, {type:"symbol",value:"b"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S002 S004 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[0].children[2], [a, b, c], {'type': 'symbol', 'value': 'c'}] After derived = [{'type': 'symbol', 'value': 'c'}, {type:"symbol",value:"c"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S003 S005 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[0].children[3], [a, b, c], {'type': 'symbol', 'value': 'a'}] After derived = [{'type': 'symbol', 'value': 'a'}, {type:"symbol",value:"a"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S004 S006 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[0].children[4], [a, b, c], {'type': 'symbol', 'value': 'b'}] After derived = [{'type': 'symbol', 'value': 'b'}, {type:"symbol",value:"b"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S005 S007 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[0], [a, b, c], {'type': 'concat', 'children': [{'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}, {'type': 'symbol', 'value': 'c'}, {'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}]}] After derived = [{'type': 'concat', 'children': [{'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}, {'type': 'symbol', 'value': 'c'}, {'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}]}, {children:[{type:"symbol",value:"a"},{type:"symbol",value:"b"},{type:"symbol",value:"c"},{type:"symbol",value:"a"},{type:"symbol",value:"b"}],type:"concat"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S006 S008 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[1].child, [a, b, c], {'type': 'symbol', 'value': 'b'}] After derived = [{'type': 'symbol', 'value': 'b'}, {type:"symbol",value:"b"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S007 S009 · impliesBefore source roles = [Regex ORIGINAL bounded.ast.children[1], [a, b, c], {'type': 'star', 'child': {'type': 'symbol', 'value': 'b'}}] After derived = [{'type': 'star', 'child': {'type': 'symbol', 'value': 'b'}}, {child:{type:"symbol",value:"b"},type:"star"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S008 S010 · impliesBefore source roles = [Regex ORIGINAL bounded.ast, [a, b, c], {'type': 'union', 'children': [{'type': 'concat', 'children': [{'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}, {'type': 'symbol', 'value': 'c'}, {'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}]}, {'type': 'star', 'child': {'type': 'symbol', 'value': 'b'}}]}] After derived = [{'type': 'union', 'children': [{'type': 'star', 'child': {'type': 'symbol', 'value': 'b'}}, {'type': 'concat', 'children': [{'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}, {'type': 'symbol', 'value': 'c'}, {'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}]}]}, {children:[{child:{type:"symbol",value:"b"},type:"star"},{children:[{type:"symbol",value:"a"},{type:"symbol",value:"b"},{type:"symbol",value:"c"},{type:"symbol",value:"a"},{type:"symbol",value:"b"}],type:"concat"}],type:"union"}] Conditions: none For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate. Step identifiers and dependenciesRule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S009 S011 · impliesBefore source roles = [[a, b, c], 5] After derived = [364] Conditions: none The bounded universe has sum |alphabet|^k words,including epsilon,and source budget<=4096.This defines complete bounded enumeration,not unbounded equivalence. Step identifiers and dependenciesRule: Regex_COMPLETE_bounded_word_universe_not_unbounded_equivalence · Uses: G001, S010 S012 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0].star_base, symbol, {'type': 'symbol', 'value': 'b'}, 5] After derived = [[[b]]] Conditions: none The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits. Step identifiers and dependenciesRule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S011 S013 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0], 5, 0, [[]], [[b]]] After derived = [[[b]], [[b], []]] Conditions: none Start with epsilon and add ALL base concatenations within the length bound.Only genuinely new words enter the next frontier.Epsilon cycles add none.The finite alphabet/length bound and4096 budget give a finite universe;completion requires an empty frontier,not an arbitrary iteration cutoff. Step identifiers and dependenciesRule: Regex_STAR_each_extensional_frontier_closure_EPS_cycles_terminate · Uses: G001, S012 S014 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0], 5, 1, [[b]], [[b]]] After derived = [[[b, b]], [[b, b], [b], []]] Conditions: none Start with epsilon and add ALL base concatenations within the length bound.Only genuinely new words enter the next frontier.Epsilon cycles add none.The finite alphabet/length bound and4096 budget give a finite universe;completion requires an empty frontier,not an arbitrary iteration cutoff. Step identifiers and dependenciesRule: Regex_STAR_each_extensional_frontier_closure_EPS_cycles_terminate · Uses: G001, S013 S015 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0], 5, 2, [[b, b]], [[b]]] After derived = [[[b, b, b]], [[b, b, b], [b, b], [b], []]] Conditions: none Start with epsilon and add ALL base concatenations within the length bound.Only genuinely new words enter the next frontier.Epsilon cycles add none.The finite alphabet/length bound and4096 budget give a finite universe;completion requires an empty frontier,not an arbitrary iteration cutoff. Step identifiers and dependenciesRule: Regex_STAR_each_extensional_frontier_closure_EPS_cycles_terminate · Uses: G001, S014 S016 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0], 5, 3, [[b, b, b]], [[b]]] After derived = [[[b, b, b, b]], [[b, b, b, b], [b, b, b], [b, b], [b], []]] Conditions: none Start with epsilon and add ALL base concatenations within the length bound.Only genuinely new words enter the next frontier.Epsilon cycles add none.The finite alphabet/length bound and4096 budget give a finite universe;completion requires an empty frontier,not an arbitrary iteration cutoff. Step identifiers and dependenciesRule: Regex_STAR_each_extensional_frontier_closure_EPS_cycles_terminate · Uses: G001, S015 S017 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0], 5, 4, [[b, b, b, b]], [[b]]] After derived = [[[b, b, b, b, b]], [[b, b, b, b, b], [b, b, b, b], [b, b, b], [b, b], [b], []]] Conditions: none Start with epsilon and add ALL base concatenations within the length bound.Only genuinely new words enter the next frontier.Epsilon cycles add none.The finite alphabet/length bound and4096 budget give a finite universe;completion requires an empty frontier,not an arbitrary iteration cutoff. Step identifiers and dependenciesRule: Regex_STAR_each_extensional_frontier_closure_EPS_cycles_terminate · Uses: G001, S016 S018 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[0], 5, 5, [[b, b, b, b, b]], [[b]]] After derived = [[], [[b, b, b, b, b], [b, b, b, b], [b, b, b], [b, b], [b], []]] Conditions: none Start with epsilon and add ALL base concatenations within the length bound.Only genuinely new words enter the next frontier.Epsilon cycles add none.The finite alphabet/length bound and4096 budget give a finite universe;completion requires an empty frontier,not an arbitrary iteration cutoff. Step identifiers and dependenciesRule: Regex_STAR_each_extensional_frontier_closure_EPS_cycles_terminate · Uses: G001, S017 S019 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1].concat[0], symbol, {'type': 'symbol', 'value': 'a'}, 5] After derived = [[[a]]] Conditions: none The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits. Step identifiers and dependenciesRule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S018 S020 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1], 0, 5, [[]], [[a]]] After derived = [[[a]]] Conditions: none In ORIGINAL concatenation order take EVERY prefix/next-child word concatenation and discard only excessive length.If total length<=m,every factor length<=m,so truncation loses no allowed combination. Step identifiers and dependenciesRule: Regex_EACH_ordered_concatenation_complete_cartesian_word_products · Uses: G001, S019 S021 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1].concat[1], symbol, {'type': 'symbol', 'value': 'b'}, 5] After derived = [[[b]]] Conditions: none The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits. Step identifiers and dependenciesRule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S020 S022 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1], 1, 5, [[a]], [[b]]] After derived = [[[a, b]]] Conditions: none In ORIGINAL concatenation order take EVERY prefix/next-child word concatenation and discard only excessive length.If total length<=m,every factor length<=m,so truncation loses no allowed combination. Step identifiers and dependenciesRule: Regex_EACH_ordered_concatenation_complete_cartesian_word_products · Uses: G001, S021 S023 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1].concat[2], symbol, {'type': 'symbol', 'value': 'c'}, 5] After derived = [[[c]]] Conditions: none The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits. Step identifiers and dependenciesRule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S022 S024 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1], 2, 5, [[a, b]], [[c]]] After derived = [[[a, b, c]]] Conditions: none In ORIGINAL concatenation order take EVERY prefix/next-child word concatenation and discard only excessive length.If total length<=m,every factor length<=m,so truncation loses no allowed combination. Step identifiers and dependenciesRule: Regex_EACH_ordered_concatenation_complete_cartesian_word_products · Uses: G001, S023 S025 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1].concat[3], symbol, {'type': 'symbol', 'value': 'a'}, 5] After derived = [[[a]]] Conditions: none The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits. Step identifiers and dependenciesRule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S024 S026 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1], 3, 5, [[a, b, c]], [[a]]] After derived = [[[a, b, c, a]]] Conditions: none In ORIGINAL concatenation order take EVERY prefix/next-child word concatenation and discard only excessive length.If total length<=m,every factor length<=m,so truncation loses no allowed combination. Step identifiers and dependenciesRule: Regex_EACH_ordered_concatenation_complete_cartesian_word_products · Uses: G001, S025 S027 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1].concat[4], symbol, {'type': 'symbol', 'value': 'b'}, 5] After derived = [[[b]]] Conditions: none The empty language has no words;epsilon has the single empty word;a symbol has its one token within the queried length bound.Words are token arrays,not reinterpreted character splits. Step identifiers and dependenciesRule: Regex_atomic_language_EMPTY_versus_EPS_versus_literal_symbol · Uses: G001, S026 S028 · impliesBefore source roles = [Regex ORIGINAL bounded.language.union[1], 4, 5, [[a, b, c, a]], [[b]]] After derived = [[[a, b, c, a, b]]] Conditions: none In ORIGINAL concatenation order take EVERY prefix/next-child word concatenation and discard only excessive length.If total length<=m,every factor length<=m,so truncation loses no allowed combination. Step identifiers and dependenciesRule: Regex_EACH_ordered_concatenation_complete_cartesian_word_products · Uses: G001, S027 S029 · impliesBefore source roles = [Regex ORIGINAL bounded.language, 5, [[[b, b, b, b, b], [b, b, b, b], [b, b, b], [b, b], [b], []], [[a, b, c, a, b]]]] After derived = [[[a, b, c, a, b], [b, b, b, b, b], [b, b, b, b], [b, b, b], [b, b], [b], []]] Conditions: none Union includes ALL child languages,retaining each word once without reordering its symbols.Structural induction accounts for inclusion/exclusion of every word within the bound. Step identifiers and dependenciesRule: Regex_union_ALL_child_languages_extensional_bound · Uses: G001, S028 ## Reverse checks - S029 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S028 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S027 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S026 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S025 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S024 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S023 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S022 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S021 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S020 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S019 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S018 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S017 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S016 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S015 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S014 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S013 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S012 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S011 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S010 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S009 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S008 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S007 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S006 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S005 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S004 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S003 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. - S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct. ## Result ([a, b, c], {children:[{child:{type:"symbol",value:"b"},type:"star"},{children:[{type:"symbol",value:"a"},{type:"symbol",value:"b"},{type:"symbol",value:"c"},{type:"symbol",value:"a"},{type:"symbol",value:"b"}],type:"concat"}],type:"union"}, 5, [[], [b], [b, b], [b, b, b], [b, b, b, b], [a, b, c, a, b], [b, b, b, b, b]], 7, Yes, epsilon_cycles_terminate_by_extensional_dedup) The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 09b0b9aafb3bf210cdea3501feb6b809fa86fa97c63e43b87118943325d2e908 - candidate record SHA-256: 5817c4b932138fdcb0347284f0bc8ccb8fcb83e27d3ab4f1bf9390591b514a1d - semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54 - question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261118-r06-regular-expression-0035.json)