After new observations of 39 galaxies at z ∼ 0.6-1.0 obtained at the IRAM 30-m telescope, we present our full CO line survey covering the redshift range 0.2 < z < 1. Our aim is to determine the driving factors accounting for the steep decline in the star formation rate during this epoch. We study both the gas fraction, defined as M gas /(M gas + M star ), and the star formation efficiency (SFE) defined by the ratio between far-infrared luminosity and molecular gas mass (L FIR /M(H 2 )), i.e. a measure for the inverse of the gas depletion time. The sources are selected to be ultra-luminous infrared galaxies (ULIRGs), with L FIR greater than 10 12 L and experiencing starbursts. When we adopt a standard ULIRG CO-to-H 2 conversion factor, their molecular gas depletion time is less than 100 Myr. Our full survey has now filled the gap of CO observations in the 0.2 < z < 1 range covering almost half of cosmic history. The detection rate in the 0.6 < z < 1 interval is 38% (15 galaxies out of 39), compared to 60% for the 0.2 < z < 0.6 interval. The average CO luminosity is L CO = 1.8 × 10 10 K km s −1 pc 2 , corresponding to an average H 2 mass of 1.45 × 10 10 M . From observation of 7 galaxies in both CO(2-1) and CO(4-3), a high gas excitation has been derived; together with the dust mass estimation, this supports the choice of our low ULIRG conversion factor between CO luminosity and H 2 for our sample sources. We find that both the gas fraction and the SFE significantly increase with redshift, by factors of 3 ± 1 from z = 0 to 1, and therefore both quantities play an important role and complement each other in cosmic star formation evolution.