New Zealand Law
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The test for getting a fixed term tenancy cancelled is quite strict under the Residentail Tenancies Act. Section 66 says
Reduction or termination of fixed-term tenancy
(1)On application by a party to a fixed-term tenancy, the Tribunal may make an order reducing the term of the tenancy by a period stated in the order, and making such variations in the terms of the tenancy as are necessary because of the reduction of the term, where it is satisfied that, because of an unforeseen change in the applicant's circumstances, the severe hardship which the applicant would suffer if the term of the tenancy were not reduced would be greater than the hardship which the other party to the tenancy would suffer if the term were reduced.
(2)Where the Tribunal makes an order under subsection (1), the Tribunal may order that the applicant pay to the other party an amount determined by the Tribunal by way of reasonable compensation for any loss or damage to the other party which would result from the reduction in the term of the tenancy.
(3)On an application by a tenant who is a party to a fixed-term tenancy, the Tribunal may make an order terminating the tenancy if the Tribunal is satisfied that the tenant has received a notice of a rent increase that—
(a)is substantial; and
(b)is of an amount that the tenant could not reasonably foresee when he or she entered into the tenancy agreement; and
(c)has caused, or will cause, serious hardship.
So you need to concentrate on why this issue will cause severe hardship to you and the unforeseen circumstances. I am not sure one issue like this rotten step would be enough, and you will need to explain carefully why this is a major problem