diff --git a/src/cutadapt/kmer_heuristic.py b/src/cutadapt/kmer_heuristic.py
index ffdf035..0b26d14 100644
--- a/src/cutadapt/kmer_heuristic.py
+++ b/src/cutadapt/kmer_heuristic.py
@@ -1,39 +1,29 @@
 import io
-import itertools
-import sys
 from typing import List, Optional, Set, Tuple
 from collections import defaultdict
 
 
-def kmer_possibilities(sequence: str, chunks: int) -> List[Set[str]]:
+def kmer_chunks(sequence: str, chunks: int) -> Set[str]:
     """
-    Partition a sequence in almost equal sized chunks. Return all possibilities.
-
-    Example sequence ABCDEFGH with 3 chunks. Possibilities:
-    ["ABC", "DEF", "GH"]; ["ABC", "DE", "FGH"]; ["AB", "CDE", "FGH"]
+    Partition a sequence in almost equal sized chunks. Returns the shortest
+    possibility. AABCABCABC, 3 returns {"AABC", "ABC"}
     """
     chunk_size = len(sequence) // (chunks)
     remainder = len(sequence) % (chunks)
     chunk_sizes: List[int] = remainder * [chunk_size + 1] + (chunks - remainder) * [
         chunk_size
     ]
-    possible_orderings = set(itertools.permutations(chunk_sizes))
-    kmer_sets = []
-    for chunk_list in possible_orderings:
-        offset = 0
-        chunk_set = set()
-        for size in chunk_list:
-            chunk_set.add(sequence[offset : offset + size])
-            offset += size
-        kmer_sets.append(chunk_set)
-    return kmer_sets
+    offset = 0
+    chunk_set = set()
+    for size in chunk_sizes:
+        chunk_set.add(sequence[offset : offset + size])
+        offset += size
+    return chunk_set
 
 
-# A SearchSet is a start and stop combined with a list of possible kmer sets
-# which should appear between this start and stop. Start and stop follow python
-# indexing rules. (Negative start is a position relative to the end. None end
-# is to the end of the sequence)
-SearchSet = Tuple[int, Optional[int], List[Set[str]]]
+# A SearchSet is a start and stop combined with a set of strings to search
+# for at that position
+SearchSet = Tuple[int, Optional[int], Set[str]]
 
 
 def minimize_kmer_search_list(
@@ -74,24 +64,22 @@ def minimize_kmer_search_list(
     return kmers_and_positions
 
 
-def find_optimal_kmers(
+def remove_redundant_kmers(
     search_sets: List[SearchSet],
 ) -> List[Tuple[int, Optional[int], List[str]]]:
-    minimal_score = sys.maxsize
-    best_combination = []
-    positions = [(start, stop) for start, stop, kmer_set_list in search_sets]
-    kmer_set_lists = [kmer_set_list for start, stop, kmer_set_list in search_sets]
-    for kmer_sets in itertools.product(*kmer_set_lists):
-        kmer_search_list = []
-        for kmer_set, (start, stop) in zip(kmer_sets, positions):
-            for kmer in kmer_set:
-                kmer_search_list.append((kmer, start, stop))
-        minimized_search_list = minimize_kmer_search_list(kmer_search_list)
-        if len(minimized_search_list) < minimal_score:
-            best_combination = minimized_search_list
-            minimal_score = len(minimized_search_list)
+    """
+    This removes kmers that are searched in multiple search sets and makes
+    sure they are only searched in the larger search set. This reduces the
+    amount of searched patterns and therefore the number of false positives.
+    """
+
+    kmer_search_list = []
+    for start, stop, kmer_set in search_sets:
+        for kmer in kmer_set:
+            kmer_search_list.append((kmer, start, stop))
+    minimized_search_list = minimize_kmer_search_list(kmer_search_list)
     result_dict = defaultdict(list)
-    for kmer, start, stop in best_combination:
+    for kmer, start, stop in minimized_search_list:
         result_dict[(start, stop)].append(kmer)
     return [(start, stop, kmers) for (start, stop), kmers in result_dict.items()]
 
@@ -120,10 +108,10 @@ def create_back_overlap_searchsets(
             min_overlap_kmer_length = 5
             if minimum_length < min_overlap_kmer_length:
                 for i in range(minimum_length, min_overlap_kmer_length):
-                    search_set = (-i, None, [{adapter[:i]}])
+                    search_set = (-i, None, {adapter[:i]})
                     search_sets.append(search_set)
                 minimum_length = min_overlap_kmer_length
-        kmer_sets = kmer_possibilities(adapter[:minimum_length], max_errors + 1)
+        kmer_sets = kmer_chunks(adapter[:minimum_length], max_errors + 1)
         search_sets.append((-length, None, kmer_sets))
         minimum_length = length + 1
     return search_sets
@@ -166,16 +154,14 @@ def create_positions_and_kmers(
             adapter[::-1], min_overlap, error_rate
         )
         front_search_sets = []
-        for start, stop, kmer_sets in reversed_back_search_sets:
-            new_kmer_sets = [
-                {kmer[::-1] for kmer in kmer_set} for kmer_set in kmer_sets
-            ]
-            front_search_sets.append((0, -start, new_kmer_sets))
+        for start, stop, kmer_set in reversed_back_search_sets:
+            new_kmer_set = {kmer[::-1] for kmer in kmer_set}
+            front_search_sets.append((0, -start, new_kmer_set))
         search_sets.extend(front_search_sets)
     if internal:
-        kmer_sets = kmer_possibilities(adapter, max_errors + 1)
+        kmer_sets = kmer_chunks(adapter, max_errors + 1)
         search_sets.append((0, None, kmer_sets))
-    return find_optimal_kmers(search_sets)
+    return remove_redundant_kmers(search_sets)
 
 
 def kmer_probability_analysis(
@@ -215,3 +201,31 @@ def kmer_probability_analysis(
         f"Chance for profile hit by random sequence: {(1 - accumulated_not_hit_chance) * 100:.2f}%\n"
     )
     return out.getvalue()
+
+
+if __name__ == "__main__":
+    # This allows for easy debugging and benchmarking of the kmer heuristic code.
+    import argparse
+    from ._kmer_finder import KmerFinder
+    import dnaio
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--adapter")
+    parser.add_argument("--anywhere", action="store_true")
+    parser.add_argument("fastq")
+    args = parser.parse_args()
+    kmers_and_offsets = create_positions_and_kmers(
+        args.adapter, 3, 0.1, back_adapter=True, front_adapter=args.anywhere
+    )
+    kmer_finder = KmerFinder(kmers_and_offsets)
+    print(kmer_probability_analysis(kmers_and_offsets))
+    with dnaio.open(args.fastq, mode="r", open_threads=0) as reader:  # type: ignore
+        number_of_records = 0
+        possible_adapters_found = 0
+        for number_of_records, record in enumerate(reader, start=1):
+            if kmer_finder.kmers_present(record.sequence):
+                possible_adapters_found += 1
+    print(
+        f"Percentage possible adapters: "
+        f"{possible_adapters_found * 100 / number_of_records:.2f}%"
+    )

diff --git a/tests/test_kmer_heuristic.py b/tests/test_kmer_heuristic.py
index 1110665..c3a69a9 100644
--- a/tests/test_kmer_heuristic.py
+++ b/tests/test_kmer_heuristic.py
@@ -1,7 +1,7 @@
 import pytest
 
 from cutadapt.kmer_heuristic import (
-    kmer_possibilities,
+    kmer_chunks,
     minimize_kmer_search_list,
     create_back_overlap_searchsets,
     create_positions_and_kmers,
@@ -11,15 +11,12 @@ from cutadapt.kmer_heuristic import (
 @pytest.mark.parametrize(
     ["sequence", "chunks", "expected"],
     [
-        ("ABC", 3, [{"A", "B", "C"}]),
-        ("ABCD", 3, [{"A", "B", "CD"}, {"A", "BC", "D"}, {"AB", "C", "D"}]),
+        ("ABC", 3, {"A", "B", "C"}),
+        ("ABCD", 3, {"AB", "C", "D"}),
     ],
 )
-def test_kmer_possibilities(sequence, chunks, expected):
-    frozen_expected = set(frozenset(s) for s in expected)
-    result = kmer_possibilities(sequence, chunks)
-    frozen_result = set(frozenset(s) for s in result)
-    assert frozen_expected == frozen_result
+def test_kmer_chunks(sequence, chunks, expected):
+    assert kmer_chunks(sequence, chunks) == expected
 
 
 @pytest.mark.parametrize(
@@ -45,11 +42,11 @@ def test_create_back_overlap_searchsets():
     adapter = "ABCDEFGHIJ0123456789"
     searchsets = create_back_overlap_searchsets(adapter, 3, 0.1)
     assert len(searchsets) == 5
-    assert (-3, None, [{"ABC"}]) in searchsets
-    assert (-4, None, [{"ABCD"}]) in searchsets
-    assert (-9, None, [{"ABCDE"}]) in searchsets
-    assert (-19, None, kmer_possibilities(adapter[:10], 2)) in searchsets
-    assert (-20, None, kmer_possibilities(adapter, 3)) in searchsets
+    assert (-3, None, {"ABC"}) in searchsets
+    assert (-4, None, {"ABCD"}) in searchsets
+    assert (-9, None, {"ABCDE"}) in searchsets
+    assert (-19, None, kmer_chunks(adapter[:10], 2)) in searchsets
+    assert (-20, None, kmer_chunks(adapter, 3)) in searchsets
 
 
 @pytest.mark.parametrize(
@@ -106,3 +103,17 @@ def test_create_kmers_and_positions(kwargs, expected):
     assert {(start, stop): frozenset(kmers) for start, stop, kmers in result} == {
         (start, stop): frozenset(kmers) for start, stop, kmers in expected
     }
+
+
+@pytest.mark.timeout(0.5)
+def test_create_positions_and_kmers_slow():
+    create_positions_and_kmers(
+        # Ridiculous size to check if there aren't any quadratic or exponential
+        # algorithms in the code.
+        "A" * 1000,
+        min_overlap=3,
+        error_rate=0.1,
+        back_adapter=True,
+        front_adapter=False,
+        internal=True,
+    )

Cutadapt 4.3 runs excruciatingly long
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### Problem description

Our CI pipeline runtime recently (and suddenly) increased from ~3 min to more than 4h. We were able to identify an interal Cutadapt call as the culprit, with each individual call taking more than 1h. We did not observe a functional deterioration, but I am not 100% sure that our CI pipeline would necessarily pick that up.

The problem occurs **only for the most recent version (`4.3`)**, not with versions `4.1` and `4.2`. Indeed, capping the range of the supported Cutadapt version to `<=4.2` restored our CI runtime back to the typical ~3 min.

### Steps to reproduce

Here is the offending call:

```bash
cutadapt -a A{100} -o out.fastq FILE
```

where `FILE` is, for example, this tiny [test file](https://raw.githubusercontent.com/zavolanlab/htsinfer/dev/tests/files/adapter_single.fastq).

#### Software information
* Python version: 3.10.0; `conda-forge` build `h12debd9_5`
* Cutadapt version: 4.3; `bioconda` buid `py310h1425a21_0`
* Installed via: Conda/Mamba

### Additional info

In our CI pipeline, the problem occurs for Python versions 3.7, 3.8 and 3.9 as well. Installation via Pip was not tested. When recreating the issue locally, one of my cores was running at 100% speed, with very little memory consumption. I did not wait for the command to conclude (my laptop got hot) and see if the output is different from that obtained for older versions (apologies!).

Looking at the changes introduced in `4.3`, my best bet would be on https://github.com/marcelm/cutadapt/pull/663 possibly being the cause of this issue.
tests/test_kmer_heuristic.py::test_kmer_chunks[ABC-3-expected0] tests/test_kmer_heuristic.py::test_kmer_chunks[ABCD-3-expected1] tests/test_kmer_heuristic.py::test_minimize_kmer_search_list[kmer_search_list0-expected0] tests/test_kmer_heuristic.py::test_minimize_kmer_search_list[kmer_search_list1-expected1] tests/test_kmer_heuristic.py::test_minimize_kmer_search_list[kmer_search_list2-expected2] tests/test_kmer_heuristic.py::test_minimize_kmer_search_list[kmer_search_list3-expected3] tests/test_kmer_heuristic.py::test_minimize_kmer_search_list[kmer_search_list4-expected4] tests/test_kmer_heuristic.py::test_minimize_kmer_search_list[kmer_search_list5-expected5] tests/test_kmer_heuristic.py::test_create_back_overlap_searchsets tests/test_kmer_heuristic.py::test_create_kmers_and_positions[kwargs0-expected0] tests/test_kmer_heuristic.py::test_create_kmers_and_positions[kwargs1-expected1] tests/test_kmer_heuristic.py::test_create_kmers_and_positions[kwargs2-expected2] tests/test_kmer_heuristic.py::test_create_kmers_and_positions[kwargs3-expected3] tests/test_kmer_heuristic.py::test_create_kmers_and_positions[kwargs4-expected4] tests/test_kmer_heuristic.py::test_create_positions_and_kmers_slow