  This paper investigates the combined effects of two distinctive power-type
nonlinear terms (with parameters $p,q>1$) in the lifespan of small solutions to
semi-linear wave equations. We determine the full region of $(p,q)$ to admit
global existence of small solutions, at least for spatial dimensions $n=2, 3$.
Moreover, for many $(p,q)$ when there is no global existence, we obtain sharp
lower bound of the lifespan, which is of the same order as the upper bound of
the lifespan.
