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a e SUB algebra ANIMAL x assume bijective clause set codomain compute congruence congruence-closed Corollary critical pairs critical sort relation deduction-closed defined Definition denoted DOM(a E-resolution elementary signatures equation system equational theory equivalence relation equivalent example finitary finite set finite signature function symbol functionally reflexive axioms Furthermore ground instances ground terms hence idempotent ill-sorted implies induction initial algebra instantiation Lemma Let a e Let F literals logic LSz(x LSz(y many-sorted many-sorted logic minimal set multiset order-sorted paramodulation predicate Proof Proposition Q-free quasi-ordering regular signatures resolution rigid E-unifier rule satisfied semilattice set of ground set of unifiers solved sort-assignment sort-decreasing sort-preserving sort-structure sorted signature step SUBR subset subsorts subterm-closed subterms system F term declarations term rewriting system Theorem undecidable unification algorithm unification problem unification procedure unsorted UV(F well-sorted substitutions well-sorted terms Z-algebra Z-assignment Z-congruence Z-homomorphism Z-model Z-renaming Z-terms Z-unification