  In this paper we study the hyperbolic and parabolic strip deformations of
ideal (possibly once-punctured) hyperbolic polygons whose vertices are
decorated with horoballs. We prove that the interiors of their arc complexes
parametrise the open convex set of all uniformly lengthening infinitesimal
deformations of the decorated hyperbolic metrics on these surfaces, motivated
by the work of Danciger-Gu\'eritaud-Kassel.
