A really early version of Mosaik for iPad , the realtime timestretching loop player by NDVR was released on the App Store today.
While it’s a very cheap download for under $1, this release isn’t quite an Ableton Live for iPad yet. You can AudioPaste a piece of audio into the app, fine-tune the automatic beat-detection, warp your audio into the BPM you desire and play or loop (a section of it) back and AudioCopy it out to another app.
NDVR promises manual adjustment of warp markers, Audiobus support, multiple tracks, realtime audio-recording and more to be added over the next updates.
While it may not be a very useful app right now, getting Mosaik for 1/8th of the regular price might make it a good investment for when it grows into a sort-of Ableton for iPad.