GeologyRocks

This is exactly what happens in a subduction zone (easier if you Google that rather than have me write it out) which produces enough heat to melt rocks to a magma, the end product of which is a volcano.  These are igneous rocks and can come from sea floor sediments.  Indeed the water content can lower the temperature at which the rocks melt.

With this you are talking of a movement of 2mm upwards (to about 10mm) per year to produce a melt, but these are incredibly vast slabs of rock. 

To a lesser extent rocks can be altered by heat and/or pressure to a point where they become 'plastic', but do not melt.  These are known as metamorphic rocks, and are arguably the most complex (but also the most interesting and beautiful - IMHO) of the three major rock groups.

In answer to your question, I don't know of any combinations of rocks that will not melt or metamorphise, given the right conditions. 

However, you will not produce either of these effects with a couple of lumps of rock in your hand.  Needs far greater forces that we can produce.

All the terms I have used may be unfamiliar to you, but I assure they are common in geology, and will come up with a full explanation if Googled  

Does this help?

 John

“Civilisation exists by geological consent, subject to change without notice.” -  Will Durant