Recycling of takeaway cups is possible, but it’s notoriously difficult. This is because the cups are a composite of plastic and paper, which are very hard to separate and separation of the two materials is necessary in order to recycle each one.
There are companies in Ireland offering compostable cups and although a better option than standard disposable coffee cups these cups need to be segregated to a compost bin in order for them to compost/ break down. If not, they can end up contaminating recycled paper streams, or end up in landfill waste.
Apart from logistical problems with recyclable or compostable takeaway cups, both of these options use up valuable resources for what is essentially a single-use item. Both require raw materials and energy to make, transport and dispose of them, these resources can never be recouped.