Krull dimension of mixed extensions

For a commutative ring RR with identity, dimRdimR shall stand for the Krull dimension of RR. It is known that dimR[x]≤2dimR+1dimR[x]≤2dimR+1. We show that this does not hold for the power series extensions. Using mixed extensions, we construct an example of a finite-dimensional integral domain RR such that 2dimR+12(n−1)/(n−2)dimD=d>2(n−1)/(n−2), then dimR〚x〛=dn+1>2dimR+1. This is an answer to the question of Coykendall and Gilmer.