On weak Zariski decompositions and termination of flips

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. Under the same hypothesis we prove that the existence of weak Zariski decompositions for pseudo-effective log canonical pairs implies the existence of weak Zariski decompositions for pseudo-effective generalized log canonical pairs. As an application, we prove the termination of any minimal model program for generalized log canonical pseudo-effective 4-folds.