  We show that the word problem for an amalgam $[S_1,S_2;U,\omega_1,\omega_2]$
of inverse semigroups may be undecidable even if we assume $S_1$ and $S_2$ (and
therefore $U$) to have finite $\mathcal{R}$-classes and $\omega_1,\omega_2$ to
be computable functions, interrupting a series of positive decidability results
on the subject. This is achieved by encoding into an appropriate amalgam of
inverse semigroups 2-counter machines with sufficient universality, and
relating the nature of certain \sch graphs to sequences of computations in the
machine.
