TITLE: speeding up Gosper and WZ algorithms
QUESTION [5 upvotes]: In our ongoing work to speed up symbolic summation and other similar algorithms in Sagemath, we notice that naive implementations of Gosper and Wilf-Zeilberger (a.k.a. WZ) algorithms are usually quite slow. 
What is the state of the art here? E.g. is there software available that can derive Clausen $_4 F_3$ identity (see (V) on p.43 of the A=B book) quickly (few seconds on a laptop, say?) using the the WZ algorithm?

REPLY [4 votes]: The group at RISC has been working aggressively towards developing improved algorithms for many computer algebra problems, including the Zeilberger's. So, it is a good place to ask.
Meantime, I just wanted to say this regarding Clausen $_4 F_3$ identity that the OP mentioned. If you read on in the book A=B, on page 127 there is a rewrite of the identity and a procedure outlined as well. I just checked it myself using a much earlier version from Zeilberger, called EKHAD, and executed in Maple. The verification of Clausen is instant!