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Context: The condensation of inorganic dust grains in the winds of evolved stars is poorly understood. As of today, it is not yet known which molecular clusters form the first dust grains in oxygen-rich (C/O < 1) asymptotic giant branch (AGB) winds. Aluminium oxides and iron-free silicates are often put forward as promising candidates for the first dust seeds. Aims: We aim to constrain the dust formation histories in the winds of oxygen-rich AGB stars. Methods: We obtained Atacama Large Millimeter/sub-millimeter array (ALMA) observations with a spatial resolution of 120 × 150mas tracing the dust formation region of the low mass-loss rate AGB star, R Dor, and the high mass-loss rate AGB star, IK Tau. We detected emission line profiles of AlO, AlOH, and AlCl in the ALMA data and used these line profiles to derive a lower limit of atomic aluminium incorporated in molecules. This constrains the aluminium budget that can condense into grains. Results: Radiative transfer models constrain the fractional abundances of AlO, AlOH, and AlCl in IK Tau and R Dor. We show that the gas-phase aluminium chemistry is completely different in both stars with a remarkable difference in the AlO and AlOH abundance stratification. The amount of aluminium locked up in these three molecules is small, ≤1.1×10−7 w.r.t. H2, for both stars, i.e. only ≤2% of the total aluminium budget. An important result is that AlO and AlOH, which are the direct precursors of alumina (Al2O3) grains, are detected well beyond the onset of the dust condensation, which proves that the aluminium oxide condensation cycle is not fully efficient. The ALMA observations allow us to quantitatively assess the current generation of theoretical dynamical-chemical models for AGB winds. We discuss how the current proposed scenario of aluminium dust condensation for low mass-loss rate AGB stars within a few stellar radii from the star, in particular for R Dor and W Hya, poses a challenge if one wishes to explain both the dust spectral features in the spectral energy distribution (SED) in interferometric data and in the polarized light signal. In particular, the estimated grain temperature of Al2O3 is too high for the grains to retain their amorphous structure. We advocate that large gas-phase (Al2O3)n clusters (n > 34) can be the potential agents of the broad 11µm feature in the SED and in the interferometric data and we propose potential formation mechanisms for these large clusters.