I am reading the book "Computation with finitely presented groups" on page 59, 
I don't know why we need only test six words? does any other words can be generated by the six words? it is seems not.
2026-03-25 06:02:09.1774418529
A question about how to check a rewriting system is confluent?
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Do you understand the definition of local confluence? You are looking for pairs of left hand sides of rules of the form $uv$ and $vw$ for strings $u,v,w$. Then, to test local confluence, you reduce the word $uvw$ in two different ways and check that the results are the same.
The six listed words are the only possible words $uvw$ arising from the three left hand sides in the rewriting system. For example, the first one $xyzx$ comes from the left hand sides $xyz$ and $yzx$ with $u=x$, $v=yz$, $w=x$.