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The response for the "/api/order/cancel" call will be an XML with the order details, in exactly the same format as a "/api/order/get" response (see item 5.2).
From the response's parameter "order_status" you will be able to determine if the order was successfully cancelled or not.
A cancelled order has the payment status "PR" (Payment Rejected). Please refer to item 5.2 for further information on the XML elements of the response.