The phase of the business cycle that includes a period of decline in GDP and rising unemployment is called a(n)

Contraction:

Explanation:

The contraction period is the time between the peak  (highest growth rate) and the trough ( the lowest growth rate).  At contraction, the GDP value declines from its peak to the lowest or negative growth rate. Contraction means a shrink in economic activities.

During contraction, the unemployment rate rising as employers lay-off workers due to reduced demand. Incomes and profits decline, and the GDP value decreases to low or negative values. The contraction period starts with a recession, which is a decline in GDP value for two consecutive quarters.