Postponement, conservation and preservation of strong normalization for generalized reduction

Postponement of ß_K-contractions and the conservation theorem do not hold for ordinary ß but have been established by de Groote for a mixture of ß with another reduction relation. In this paper, de Groote's results are generalized for a single reduction relation ß_e which generalizes ß. We show moreover, that ß_e has the preservation of strong normalization property.