  Let R be a commutative noetherian ring. In this paper, we study, for the
singularity category of R, the vanishing of the complexity $\delta_t(X,Y)$ in
the sense of Dimitrov, Haiden, Katzarkov and Kontsevich. We prove that the set
of real numbers t such that $\delta_t(X,Y)$ does not vanish is bounded in
various cases. We do it by building the high syzygy modules and maximal
Cohen-Macaulay modules out of a single module only by taking direct summands
and extensions.
