An algorithmic framework is presented to find an extended tree of nonlocally related systems
for a given system of differential equations (DEs). Each system in an extended tree is
equivalent in the sense that the solution set for any system in a tree can be found from the
solution set for any other system in the tree. Useful conservation laws play an essential role
in the construction of an extended tree. A useful conservation law yields potential variables
and equivalent nonlocally related potential systems and subsystems for any given system …