ABSTRACT
Example 15.2.4 We choose X2, and let E contain two operation symbols, one binary and one nullary. Let A = (V4, e) be the Klein-four group. Let
{eA} and QA(f) = eA (the identity element eA considered as binary term operation). Then we have aA[xi] = 4,A, for i = 1,2. Inductively, when t = f (ti,t2), for some ti,t2 E WE(X2), we have (aAr[t] = (uAr[f (ti, t2)] = a A (f)((cf Aritib(crA) [t2]) = eA((aAr[ti],(o-A)"[t2]) = eA. This shows that T (HA) = WE
, x2 }. The following proposition connects tree-hyperrecognizers with identities and varieties. We recall the notation IdA for the set of identities of the algebra A and SA for the term operation on A induced by a term s.
