  All known structural extensions of the substructural logic $\mathsf{FL_e}$,
Full Lambek calculus with exchange/commutativity, (corresponding to
subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot,
1\}$-equations) have decidable theoremhood; in particular all the ones defined
by knotted axioms enjoy strong decidability properties (such as the finite
embeddability property). We provide infinitely many such extensions that have
undecidable theoremhood, by encoding machines with undecidable halting problem.
An even bigger class of extensions is shown to have undecidable deducibility
problem (the corresponding varieties of residuated lattices have undecidable
word problem); actually with very few exceptions, such as the knotted axioms
and the other prespinal axioms, we prove that undecidability is ubiquitous.
Known undecidability results for non-commutative extensions use an encoding
that fails in the presence of commutativity, so and-branching counter machines
are employed. Even these machines provide encodings that fail to capture proper
extensions of commutativity, therefore we introduce a new variant that works on
an exponential scale. The correctness of the encoding is established by
employing the theory of residuated frames.
