 Take \(C\) to be the class of monoids. The term algebra determined by the binary operation symbol and the constant symbol for identity can be viewed as binary trees with variables and copies of the constant symbol at the leaves. Identifying trees according to associativity has the effect of flattening the trees into words that ignore the order in which the operation was applied (without however reversing the order of any arguments). This produces words over the alphabet \(X\) together with the identity. The identity laws then erase the identities, except in the case of a word consisting only of the identity symbol, which we take to be the empty word.