  We introduce a family of local models of dynamics based on ``word problems''
from computer science and group theory, for which we can place rigorous lower
bounds on relaxation timescales. These models can be regarded either as random
circuit or local Hamiltonian dynamics, and include many familiar examples of
constrained dynamics as special cases. The configuration space of these models
splits into dynamically disconnected sectors, and for initial states to relax,
they must ``work out'' the other states in the sector to which they belong.
When this problem has a high time complexity, relaxation is slow. In some of
the cases we study, this problem also has high space complexity. When the space
complexity is larger than the system size, an unconventional type of jamming
transition can occur, whereby a system of a fixed size is not ergodic, but can
be made ergodic by appending a large reservoir of sites in a trivial product
state. This manifests itself in a new type of Hilbert space fragmentation that
we call fragile fragmentation. We present explicit examples where slow
relaxation and jamming strongly modify the hydrodynamics of conserved
densities. In one example, density modulations of wavevector $q$ exhibit almost
no relaxation until times $O(\exp(1/q))$, at which point they abruptly
collapse. We also comment on extensions of our results to higher dimensions.
