FA-68441 / Toll and parking fee computation / Open access

Time-band rate with calendar day cap: the daily maximum caps the whole stay once · case 01

Time-band rate with calendar day cap returns a wrong result when the daily maximum caps the whole stay once.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Multi-day stays are capped at a single daily maximum.

THE FAILURE

Multi-day stays are capped at a single daily maximum.

Unsuccessful approach: Removing the cap overcharges any day whose band charges exceed daily_max.

Case contract

Input {bands: [[start minute of day, cents per quarter hour]] sorted with first start 0, entry, exit (absolute minutes), daily_max}. Minutes of the stay are totalled per calendar day and band; each total is rounded up to whole quarter hours and priced at its band rate. Each calendar day's charge is capped at daily_max.

Why this case matters

Fee engines bill customers in integer cents; a wrong boundary, rounding stage or cap scope silently over- or under-charges.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    bands = x['bands']
    per = {}
    t = x['entry']
    while t < x['exit']:
        day, tod = divmod(t, 1440)
        i = max(k for k in range(len(bands)) if bands[k][0] <= tod)
        nxt = bands[i + 1][0] if i + 1 < len(bands) else 1440
        step = min(x['exit'] - t, nxt - tod)
        key = (day, bands[i][1])
        per[key] = per.get(key, 0) + step
        t += step
    days = {}
    for (day, rate), m in per.items():
        days[day] = days.get(day, 0) + -(-m // 15) * rate
    return min(sum(days.values()), x['daily_max'])
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'bands': [[0, 25], [1290, 50]], 'entry': 895, 'exit': 2743, 'daily_max': 2500}, 3375), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [60, 25], [900, 50], [1410, 50]], 'entry': 1980, 'exit': 2097, 'daily_max': 1500}, 200), ({'bands': [[0, 50], [390, 50], [810, 100]], 'entry': 261, 'exit': 1911, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [1410, 25]], 'entry': 43, 'exit': 1160, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [360, 100], [570, 50], [750, 25]], 'entry': 1882, 'exit': 4277, 'daily_max': 1500}, 3000)], [({'bands': [[0, 25], [1260, 100], [1410, 50]], 'entry': 202, 'exit': 2677, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [780, 50]], 'entry': 342, 'exit': 1611, 'daily_max': 1500}, 1800), ({'bands': [[0, 25], [1140, 50]], 'entry': 231, 'exit': 350, 'daily_max': 4000}, 200), ({'bands': [[0, 50], [270, 100], [570, 50], [1200, 25]], 'entry': 833, 'exit': 1582, 'daily_max': 2500}, 2150), ({'bands': [[0, 25], [750, 100]], 'entry': 788, 'exit': 1556, 'daily_max': 4000}, 4200), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500)], [({'bands': [[0, 25], [330, 100], [990, 100]], 'entry': 1845, 'exit': 1894, 'daily_max': 4000}, 400), ({'bands': [[0, 50], [750, 50], [1110, 25]], 'entry': 602, 'exit': 2580, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [270, 25], [390, 50], [930, 100]], 'entry': 1006, 'exit': 2590, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [450, 50], [1050, 25]], 'entry': 1879, 'exit': 4090, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [90, 100], [1230, 100]], 'entry': 1447, 'exit': 1546, 'daily_max': 1500}, 350)], [({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [150, 50], [300, 100], [1260, 100]], 'entry': 268, 'exit': 1452, 'daily_max': 4000}, 4025), ({'bands': [[0, 50], [210, 50], [840, 100], [1170, 50]], 'entry': 1552, 'exit': 4168, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [180, 25], [1260, 50]], 'entry': 1244, 'exit': 3629, 'daily_max': 4000}, 4600), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 25], [780, 50]], 'entry': 1711, 'exit': 2270, 'daily_max': 4000}, 1050), ({'bands': [[0, 25], [420, 50]], 'entry': 1579, 'exit': 1614, 'daily_max': 1500}, 75)], [({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [180, 25], [900, 50], [1230, 100]], 'entry': 310, 'exit': 2308, 'daily_max': 2500}, 3950), ({'bands': [[0, 25], [1170, 50]], 'entry': 263, 'exit': 547, 'daily_max': 1500}, 475), ({'bands': [[0, 25], [270, 25], [660, 50]], 'entry': 200, 'exit': 1095, 'daily_max': 2500}, 2225), ({'bands': [[0, 25], [1230, 100]], 'entry': 1750, 'exit': 4442, 'daily_max': 2500}, 5225), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [90, 50], [270, 50]], 'entry': 291, 'exit': 1639, 'daily_max': 1500}, 2050)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('fee oracle' + ' %d' % i, 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
fee oracle 0	`2500`	`3375`	Failed
fee oracle 1	`4550`	`4550`	Passed
fee oracle 2	`500`	`500`	Passed
fee oracle 3	`4000`	`4000`	Passed
fee oracle 4	`200`	`200`	Passed
fee oracle 5	`1500`	`3000`	Failed
fee oracle 6	`1500`	`1500`	Passed
fee oracle 7	`1500`	`3000`	Failed

SHA-256 / 1c574f8715f8ef95fb6e2f218b6aa15d5e74d786c971d076c7d321c6f4905e72

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    bands = x['bands']
    per = {}
    t = x['entry']
    while t < x['exit']:
        day, tod = divmod(t, 1440)
        i = max(k for k in range(len(bands)) if bands[k][0] <= tod)
        nxt = bands[i + 1][0] if i + 1 < len(bands) else 1440
        step = min(x['exit'] - t, nxt - tod)
        key = (day, bands[i][1])
        per[key] = per.get(key, 0) + step
        t += step
    days = {}
    for (day, rate), m in per.items():
        days[day] = days.get(day, 0) + -(-m // 15) * rate
    return sum(days.values())
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'bands': [[0, 25], [1290, 50]], 'entry': 895, 'exit': 2743, 'daily_max': 2500}, 3375), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [60, 25], [900, 50], [1410, 50]], 'entry': 1980, 'exit': 2097, 'daily_max': 1500}, 200), ({'bands': [[0, 50], [390, 50], [810, 100]], 'entry': 261, 'exit': 1911, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [1410, 25]], 'entry': 43, 'exit': 1160, 'daily_max': 1500}, 1500), ({'bands': [[0, 25], [360, 100], [570, 50], [750, 25]], 'entry': 1882, 'exit': 4277, 'daily_max': 1500}, 3000)], [({'bands': [[0, 25], [1260, 100], [1410, 50]], 'entry': 202, 'exit': 2677, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [780, 50]], 'entry': 342, 'exit': 1611, 'daily_max': 1500}, 1800), ({'bands': [[0, 25], [1140, 50]], 'entry': 231, 'exit': 350, 'daily_max': 4000}, 200), ({'bands': [[0, 50], [270, 100], [570, 50], [1200, 25]], 'entry': 833, 'exit': 1582, 'daily_max': 2500}, 2150), ({'bands': [[0, 25], [750, 100]], 'entry': 788, 'exit': 1556, 'daily_max': 4000}, 4200), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500)], [({'bands': [[0, 25], [330, 100], [990, 100]], 'entry': 1845, 'exit': 1894, 'daily_max': 4000}, 400), ({'bands': [[0, 50], [750, 50], [1110, 25]], 'entry': 602, 'exit': 2580, 'daily_max': 1500}, 3000), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 50], [270, 25], [390, 50], [930, 100]], 'entry': 1006, 'exit': 2590, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [450, 50], [1050, 25]], 'entry': 1879, 'exit': 4090, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [90, 100], [1230, 100]], 'entry': 1447, 'exit': 1546, 'daily_max': 1500}, 350)], [({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [150, 50], [300, 100], [1260, 100]], 'entry': 268, 'exit': 1452, 'daily_max': 4000}, 4025), ({'bands': [[0, 50], [210, 50], [840, 100], [1170, 50]], 'entry': 1552, 'exit': 4168, 'daily_max': 2500}, 5000), ({'bands': [[0, 25], [180, 25], [1260, 50]], 'entry': 1244, 'exit': 3629, 'daily_max': 4000}, 4600), ({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 25], [780, 50]], 'entry': 1711, 'exit': 2270, 'daily_max': 4000}, 1050), ({'bands': [[0, 25], [420, 50]], 'entry': 1579, 'exit': 1614, 'daily_max': 1500}, 75)], [({'bands': [[0, 25], [420, 100], [1080, 50]], 'entry': 400, 'exit': 1100, 'daily_max': 4000}, 4000), ({'bands': [[0, 50], [720, 100]], 'entry': 1400, 'exit': 1500, 'daily_max': 1500}, 500), ({'bands': [[0, 25], [180, 25], [900, 50], [1230, 100]], 'entry': 310, 'exit': 2308, 'daily_max': 2500}, 3950), ({'bands': [[0, 25], [1170, 50]], 'entry': 263, 'exit': 547, 'daily_max': 1500}, 475), ({'bands': [[0, 25], [270, 25], [660, 50]], 'entry': 200, 'exit': 1095, 'daily_max': 2500}, 2225), ({'bands': [[0, 25], [1230, 100]], 'entry': 1750, 'exit': 4442, 'daily_max': 2500}, 5225), ({'bands': [[0, 25], [420, 100], [1080, 25]], 'entry': 350, 'exit': 1100, 'daily_max': 9000}, 4550), ({'bands': [[0, 25], [90, 50], [270, 50]], 'entry': 291, 'exit': 1639, 'daily_max': 1500}, 2050)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('fee oracle' + ' %d' % i, 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
fee oracle 0	`3375`	`3375`	Passed
fee oracle 1	`4550`	`4550`	Passed
fee oracle 2	`500`	`500`	Passed
fee oracle 3	`4550`	`4000`	Failed
fee oracle 4	`200`	`200`	Passed
fee oracle 5	`7650`	`3000`	Failed
fee oracle 6	`1875`	`1500`	Failed
fee oracle 7	`6350`	`3000`	Failed

SHA-256 / 40e56b14fac00158054b439515ef3a5e2fb87a4bb75527f22f19a5e36c20b6c6

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

A deterministic, bounded toy model with a stipulated contract; it makes no claim of conformance to any agency manual or standard. 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 2026-09-29T14:48:02.216291+00:00.

Case digest / 00b925d13a4a28bcedd79bbc8712c8a865e6394ee4a590137dc714b898cf95f5