FA-93901 / Shift rostering labor rules / Open access
Exactly ten-hour spread earns the spread premium · case 01
A day spanning precisely ten hours is paid an extra hour.
ROOT CAUSE
The spread premium comparison is inclusive at 600 minutes.
VERIFIED REPAIR
Pay the spread premium only when the spread strictly exceeds 600 minutes.
Unsuccessful approach: Also requiring a split denies the premium to continuous shifts longer than ten hours.
Case contract
Worked segments [start, end] of one workday (unordered, possibly overlapping) and a minimum wage in cents. Overlapping or touching segments merge. Spread is last end minus first start. Each gap longer than 60 minutes is a split. A spread over 600 minutes earns one hour of minimum wage and replaces any split premium; otherwise each split earns min_wage // 2, for at most two splits. Return [spread, splits, premium].
Why this case matters
Spread-of-hours and split-shift premiums are frequent roster-pay rules that depend on correct interval handling.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(segments, min_wage):
seg = sorted(segments)
merged = []
for s, e in seg:
if merged and s <= merged[-1][1]:
merged[-1][1] = max(merged[-1][1], e)
else:
merged.append([s, e])
spread = merged[-1][1] - merged[0][0]
splits = sum(1 for a, b in zip(merged, merged[1:]) if b[0] - a[1] > 60)
if spread >= 600:
premium = min_wage
else:
premium = (min_wage // 2) * min(splits, 2)
return [spread, splits, premium]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: spread threshold requires split 1', [[[480, 720], [780, 1080]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[720, 960], [360, 480]], 1600], [600, 1, 800]),
('partial repair guard 3', [[[810, 1110], [480, 780]], 1520], [630, 0, 1520]),
('boundary control 4', [[[420, 1020]], 1600], [600, 0, 0]),
('boundary control 5', [[[420, 480], [550, 600], [700, 760], [840, 900], [980, 1010]], 1655],
[590, 4, 1654]),
('normal control 6', [[[720, 900], [420, 720], [961, 1141]], 1520], [721, 1, 1520]),
('normal control 7', [[[1079, 1319], [960, 1020], [420, 540], [630, 870]], 1600], [899, 2, 1600]),
('normal control 8', [[[1169, 1349], [810, 930], [990, 1110], [480, 780]], 1600], [869, 0, 1600])],
[('regression: spread threshold requires split 1', [[[480, 720], [781, 1080]], 1600], [600, 1, 800]),
('regression variant: spread threshold requires split 2', [[[420, 600], [660, 780], [840, 1020]], 1701],
[600, 0, 0]),
('partial repair guard 3', [[[719, 839], [1108, 1168], [480, 660], [898, 1078]], 1600], [688, 0, 1600]),
('boundary control 4', [[[900, 1000], [420, 600], [700, 800]], 1520], [580, 2, 1520]),
('normal control 5', [[[960, 1140], [970, 980], [480, 780]], 1520], [660, 1, 1520]),
('normal control 6', [[[420, 540], [570, 630], [691, 991], [510, 570]], 1600], [571, 1, 800]),
('normal control 7', [[[1261, 1441], [430, 440], [780, 1020], [420, 660], [1081, 1261]], 1600],
[1021, 2, 1600]),
('normal control 8', [[[480, 720], [780, 840]], 1655], [360, 0, 0])],
[('regression: spread threshold requires split 1', [[[420, 600], [660, 780], [840, 1020]], 1701],
[600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[660, 960], [370, 380], [360, 600]], 1600],
[600, 0, 0]),
('partial repair guard 3', [[[1169, 1349], [810, 930], [990, 1110], [480, 780]], 1600], [869, 0, 1600]),
('boundary control 4', [[[600, 630], [700, 730], [800, 830], [900, 930]], 1701], [330, 3, 1700]),
('boundary control 5', [[[420, 1021]], 1600], [601, 0, 1600]),
('normal control 6', [[[600, 780], [420, 480], [430, 440]], 1600], [360, 1, 800]),
('normal control 7', [[[1021, 1261], [781, 961], [480, 720]], 1600], [781, 1, 1600]),
('normal control 8', [[[810, 930], [1170, 1470], [420, 720]], 1655], [1050, 2, 1655])],
[('regression: spread threshold requires split 1', [[[420, 1020]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[480, 720], [781, 1080]], 1600], [600, 1, 800]),
('partial repair guard 3', [[[600, 780], [1139, 1379], [839, 1079]], 1701], [779, 0, 1701]),
('boundary control 4', [[[420, 600], [660, 780], [840, 1020]], 1701], [600, 0, 0]),
('boundary control 5', [[[420, 450], [520, 550], [620, 650], [720, 750]], 1600], [330, 3, 1600]),
('normal control 6', [[[480, 600]], 1655], [120, 0, 0]),
('normal control 7', [[[480, 720], [900, 1020]], 1600], [540, 1, 800]),
('normal control 8', [[[600, 840]], 1520], [240, 0, 0])],
[('regression: spread threshold requires split 1', [[[660, 960], [360, 600]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[780, 960], [360, 540]], 1655], [600, 1, 827]),
('partial repair guard 3', [[[810, 1110], [480, 780]], 1520], [630, 0, 1520]),
('boundary control 4', [[[600, 900], [610, 620], [1000, 1100]], 1655], [500, 1, 827]),
('boundary control 5', [[[480, 720], [780, 1080]], 1600], [600, 0, 0]),
('normal control 6', [[[1019, 1259], [1320, 1440], [720, 960], [360, 540]], 1655], [1080, 2, 1655]),
('normal control 7', [[[420, 600], [430, 440]], 1701], [180, 0, 0]),
('normal control 8', [[[1440, 1500], [1080, 1200], [870, 1110], [480, 780]], 1655], [1020, 2, 1655])]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: spread threshold requires split 1 | [600, 0, 1600] | [600, 0, 0] | Failed |
| regression variant: spread threshold requires split 2 | [600, 1, 1600] | [600, 1, 800] | Failed |
| partial repair guard 3 | [630, 0, 1520] | [630, 0, 1520] | Passed |
| boundary control 4 | [600, 0, 1600] | [600, 0, 0] | Failed |
| boundary control 5 | [590, 4, 1654] | [590, 4, 1654] | Passed |
| normal control 6 | [721, 1, 1520] | [721, 1, 1520] | Passed |
| normal control 7 | [899, 2, 1600] | [899, 2, 1600] | Passed |
| normal control 8 | [869, 0, 1600] | [869, 0, 1600] | Passed |
SHA-256 / ea772d78da46ba1173fd104cbf63f75aeae387d49cb53d6d2464ab3bd23cda0f
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(segments, min_wage):
seg = sorted(segments)
merged = []
for s, e in seg:
if merged and s <= merged[-1][1]:
merged[-1][1] = max(merged[-1][1], e)
else:
merged.append([s, e])
spread = merged[-1][1] - merged[0][0]
splits = sum(1 for a, b in zip(merged, merged[1:]) if b[0] - a[1] > 60)
if spread > 600 and splits:
premium = min_wage
else:
premium = (min_wage // 2) * min(splits, 2)
return [spread, splits, premium]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: spread threshold requires split 1', [[[480, 720], [780, 1080]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[720, 960], [360, 480]], 1600], [600, 1, 800]),
('partial repair guard 3', [[[810, 1110], [480, 780]], 1520], [630, 0, 1520]),
('boundary control 4', [[[420, 1020]], 1600], [600, 0, 0]),
('boundary control 5', [[[420, 480], [550, 600], [700, 760], [840, 900], [980, 1010]], 1655],
[590, 4, 1654]),
('normal control 6', [[[720, 900], [420, 720], [961, 1141]], 1520], [721, 1, 1520]),
('normal control 7', [[[1079, 1319], [960, 1020], [420, 540], [630, 870]], 1600], [899, 2, 1600]),
('normal control 8', [[[1169, 1349], [810, 930], [990, 1110], [480, 780]], 1600], [869, 0, 1600])],
[('regression: spread threshold requires split 1', [[[480, 720], [781, 1080]], 1600], [600, 1, 800]),
('regression variant: spread threshold requires split 2', [[[420, 600], [660, 780], [840, 1020]], 1701],
[600, 0, 0]),
('partial repair guard 3', [[[719, 839], [1108, 1168], [480, 660], [898, 1078]], 1600], [688, 0, 1600]),
('boundary control 4', [[[900, 1000], [420, 600], [700, 800]], 1520], [580, 2, 1520]),
('normal control 5', [[[960, 1140], [970, 980], [480, 780]], 1520], [660, 1, 1520]),
('normal control 6', [[[420, 540], [570, 630], [691, 991], [510, 570]], 1600], [571, 1, 800]),
('normal control 7', [[[1261, 1441], [430, 440], [780, 1020], [420, 660], [1081, 1261]], 1600],
[1021, 2, 1600]),
('normal control 8', [[[480, 720], [780, 840]], 1655], [360, 0, 0])],
[('regression: spread threshold requires split 1', [[[420, 600], [660, 780], [840, 1020]], 1701],
[600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[660, 960], [370, 380], [360, 600]], 1600],
[600, 0, 0]),
('partial repair guard 3', [[[1169, 1349], [810, 930], [990, 1110], [480, 780]], 1600], [869, 0, 1600]),
('boundary control 4', [[[600, 630], [700, 730], [800, 830], [900, 930]], 1701], [330, 3, 1700]),
('boundary control 5', [[[420, 1021]], 1600], [601, 0, 1600]),
('normal control 6', [[[600, 780], [420, 480], [430, 440]], 1600], [360, 1, 800]),
('normal control 7', [[[1021, 1261], [781, 961], [480, 720]], 1600], [781, 1, 1600]),
('normal control 8', [[[810, 930], [1170, 1470], [420, 720]], 1655], [1050, 2, 1655])],
[('regression: spread threshold requires split 1', [[[420, 1020]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[480, 720], [781, 1080]], 1600], [600, 1, 800]),
('partial repair guard 3', [[[600, 780], [1139, 1379], [839, 1079]], 1701], [779, 0, 1701]),
('boundary control 4', [[[420, 600], [660, 780], [840, 1020]], 1701], [600, 0, 0]),
('boundary control 5', [[[420, 450], [520, 550], [620, 650], [720, 750]], 1600], [330, 3, 1600]),
('normal control 6', [[[480, 600]], 1655], [120, 0, 0]),
('normal control 7', [[[480, 720], [900, 1020]], 1600], [540, 1, 800]),
('normal control 8', [[[600, 840]], 1520], [240, 0, 0])],
[('regression: spread threshold requires split 1', [[[660, 960], [360, 600]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[780, 960], [360, 540]], 1655], [600, 1, 827]),
('partial repair guard 3', [[[810, 1110], [480, 780]], 1520], [630, 0, 1520]),
('boundary control 4', [[[600, 900], [610, 620], [1000, 1100]], 1655], [500, 1, 827]),
('boundary control 5', [[[480, 720], [780, 1080]], 1600], [600, 0, 0]),
('normal control 6', [[[1019, 1259], [1320, 1440], [720, 960], [360, 540]], 1655], [1080, 2, 1655]),
('normal control 7', [[[420, 600], [430, 440]], 1701], [180, 0, 0]),
('normal control 8', [[[1440, 1500], [1080, 1200], [870, 1110], [480, 780]], 1655], [1020, 2, 1655])]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: spread threshold requires split 1 | [600, 0, 0] | [600, 0, 0] | Passed |
| regression variant: spread threshold requires split 2 | [600, 1, 800] | [600, 1, 800] | Passed |
| partial repair guard 3 | [630, 0, 0] | [630, 0, 1520] | Failed |
| boundary control 4 | [600, 0, 0] | [600, 0, 0] | Passed |
| boundary control 5 | [590, 4, 1654] | [590, 4, 1654] | Passed |
| normal control 6 | [721, 1, 1520] | [721, 1, 1520] | Passed |
| normal control 7 | [899, 2, 1600] | [899, 2, 1600] | Passed |
| normal control 8 | [869, 0, 0] | [869, 0, 1600] | Failed |
SHA-256 / 7d45b32b6fb04029717cd5aa696d5f5974fd4e966fd9c6a67dbef2602c5c3982
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(segments, min_wage):
seg = sorted(segments)
merged = []
for s, e in seg:
if merged and s <= merged[-1][1]:
merged[-1][1] = max(merged[-1][1], e)
else:
merged.append([s, e])
spread = merged[-1][1] - merged[0][0]
splits = sum(1 for a, b in zip(merged, merged[1:]) if b[0] - a[1] > 60)
if spread > 600:
premium = min_wage
else:
premium = (min_wage // 2) * min(splits, 2)
return [spread, splits, premium]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: spread threshold requires split 1', [[[480, 720], [780, 1080]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[720, 960], [360, 480]], 1600], [600, 1, 800]),
('partial repair guard 3', [[[810, 1110], [480, 780]], 1520], [630, 0, 1520]),
('boundary control 4', [[[420, 1020]], 1600], [600, 0, 0]),
('boundary control 5', [[[420, 480], [550, 600], [700, 760], [840, 900], [980, 1010]], 1655],
[590, 4, 1654]),
('normal control 6', [[[720, 900], [420, 720], [961, 1141]], 1520], [721, 1, 1520]),
('normal control 7', [[[1079, 1319], [960, 1020], [420, 540], [630, 870]], 1600], [899, 2, 1600]),
('normal control 8', [[[1169, 1349], [810, 930], [990, 1110], [480, 780]], 1600], [869, 0, 1600])],
[('regression: spread threshold requires split 1', [[[480, 720], [781, 1080]], 1600], [600, 1, 800]),
('regression variant: spread threshold requires split 2', [[[420, 600], [660, 780], [840, 1020]], 1701],
[600, 0, 0]),
('partial repair guard 3', [[[719, 839], [1108, 1168], [480, 660], [898, 1078]], 1600], [688, 0, 1600]),
('boundary control 4', [[[900, 1000], [420, 600], [700, 800]], 1520], [580, 2, 1520]),
('normal control 5', [[[960, 1140], [970, 980], [480, 780]], 1520], [660, 1, 1520]),
('normal control 6', [[[420, 540], [570, 630], [691, 991], [510, 570]], 1600], [571, 1, 800]),
('normal control 7', [[[1261, 1441], [430, 440], [780, 1020], [420, 660], [1081, 1261]], 1600],
[1021, 2, 1600]),
('normal control 8', [[[480, 720], [780, 840]], 1655], [360, 0, 0])],
[('regression: spread threshold requires split 1', [[[420, 600], [660, 780], [840, 1020]], 1701],
[600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[660, 960], [370, 380], [360, 600]], 1600],
[600, 0, 0]),
('partial repair guard 3', [[[1169, 1349], [810, 930], [990, 1110], [480, 780]], 1600], [869, 0, 1600]),
('boundary control 4', [[[600, 630], [700, 730], [800, 830], [900, 930]], 1701], [330, 3, 1700]),
('boundary control 5', [[[420, 1021]], 1600], [601, 0, 1600]),
('normal control 6', [[[600, 780], [420, 480], [430, 440]], 1600], [360, 1, 800]),
('normal control 7', [[[1021, 1261], [781, 961], [480, 720]], 1600], [781, 1, 1600]),
('normal control 8', [[[810, 930], [1170, 1470], [420, 720]], 1655], [1050, 2, 1655])],
[('regression: spread threshold requires split 1', [[[420, 1020]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[480, 720], [781, 1080]], 1600], [600, 1, 800]),
('partial repair guard 3', [[[600, 780], [1139, 1379], [839, 1079]], 1701], [779, 0, 1701]),
('boundary control 4', [[[420, 600], [660, 780], [840, 1020]], 1701], [600, 0, 0]),
('boundary control 5', [[[420, 450], [520, 550], [620, 650], [720, 750]], 1600], [330, 3, 1600]),
('normal control 6', [[[480, 600]], 1655], [120, 0, 0]),
('normal control 7', [[[480, 720], [900, 1020]], 1600], [540, 1, 800]),
('normal control 8', [[[600, 840]], 1520], [240, 0, 0])],
[('regression: spread threshold requires split 1', [[[660, 960], [360, 600]], 1600], [600, 0, 0]),
('regression variant: spread threshold requires split 2', [[[780, 960], [360, 540]], 1655], [600, 1, 827]),
('partial repair guard 3', [[[810, 1110], [480, 780]], 1520], [630, 0, 1520]),
('boundary control 4', [[[600, 900], [610, 620], [1000, 1100]], 1655], [500, 1, 827]),
('boundary control 5', [[[480, 720], [780, 1080]], 1600], [600, 0, 0]),
('normal control 6', [[[1019, 1259], [1320, 1440], [720, 960], [360, 540]], 1655], [1080, 2, 1655]),
('normal control 7', [[[420, 600], [430, 440]], 1701], [180, 0, 0]),
('normal control 8', [[[1440, 1500], [1080, 1200], [870, 1110], [480, 780]], 1655], [1020, 2, 1655])]]
for label, args, expected in fixtures[N-1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: spread threshold requires split 1 | [600, 0, 0] | [600, 0, 0] | Passed |
| regression variant: spread threshold requires split 2 | [600, 1, 800] | [600, 1, 800] | Passed |
| partial repair guard 3 | [630, 0, 1520] | [630, 0, 1520] | Passed |
| boundary control 4 | [600, 0, 0] | [600, 0, 0] | Passed |
| boundary control 5 | [590, 4, 1654] | [590, 4, 1654] | Passed |
| normal control 6 | [721, 1, 1520] | [721, 1, 1520] | Passed |
| normal control 7 | [899, 2, 1600] | [899, 2, 1600] | Passed |
| normal control 8 | [869, 0, 1600] | [869, 0, 1600] | Passed |
SHA-256 / 44ea18630b5c12473528f9a9fbdd31a89bffc1b97ab91513dafaf8c26c675ab2
Verification & scope
Stipulated toy labor rule for a bounded roster model; it is not legal advice and does not claim conformance with any jurisdiction, award, or collective agreement. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:51:59.387911+00:00.
Case digest / bb9d96fecff5d34398949918e916075ba0e1e1ef7566d47f3363733b517da8ab