In this talk we introduce a class of groups represented as quotient groups

of some free groups generated by infinitely many elements and certain normal

subgroups. We show that the related word problem is universal in the Blum-Shub-Smale model

of computation, i.e. it has the same difficulty as the real Halting Problem.

This is the first natural example of a problem with this property.

The work has been done jointly with Martin Ziegler.