A new elementary algorithm for proving q-hypergeometric identities

We give a fast elementary algorithm to get a small number n1 for an admissible q-proper-hypergeometric identity such that we can prove the identity by checking its correctness for n (n0≤n≤n1). For example, we get n1=191 for the q-Vandermonde-Chu identity, n1=70 for a finite version of Jacobi’s triple product identity and n1=209 for an identity due to L.J. Rogers.