Rock Cycle: Igneous Rock with erosion give sediments which will compact to give Sedimentary Rock which with heat and pressure give Metamorphic Rocks which will melt with heat and pressure to give magma
No. It's the Metamorphic rocks that melt and become magma.
magma
The transition form magma to rock is a process of cooling.
Intrusive Igneous rocks
Cooling to a solid.
magma
Metamorphic rocks can melt into magma and then undergo cooling and crystallization to become an igneous rock. Or, they can undergo weathering and erosion into sediments and then lithify to become sedimentary rocks. +++ They can melt and become magma only if subducted - a process normally confined to the sea-floor plate.
Regional Metamorphism
Igneous rocks are formed when magma solidifies, or becomes solid. Rocks become magma when they undergo extreme heat.
Magma tends to rise towards Earth's surface primarily because rocks become less dense when they melt. The hotter the magma, the more the rocks are likely to "float," if you will.
erosion
By Magma I'm guessing you mean the molten sedimentary rocks. The process is called metamorphism.