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We expand the theory of log canonical 3-fold complements. More precisely, fix a set Λ ⊂ Q satisfying the descending chain condition with Λ ⊂ Q, and let (X, B + B ′ ) be a log canonical 3-fold with coeff(B) ∈ Λ and K X + B Q-Cartier. Then, there exists a natural number n, only depending on Λ, such that the following holds. Given a contraction f : X → T and t ∈ T with K X + B + B ′ ∼ Q 0 over t, there exists Γ ≥ 0 such that Γ ∼ −n(K X + B) over t ∈ T , and (X, B + Γ/n) is log canonical.

We prove that termination of lower dimensional flips for generalized klt pairs implies termination of flips for log canonical generalized pairs with a weak Zariski decomposition. Moreover, we prove that the existence of weak Zariski decompositions for pseudo-effective klt pairs implies the existence of minimal models for such pairs.

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