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Location: Chapter 21, solution to Problem 2, second paragraph

It is (solution, second method)

Using the second method, you should get the solution \(W'W'\), where \(W'\) is the converse warbler -- \(W'xy = yxx\). If you get \(CW(CW)\) you are also right, since \(CW\) is a converse warbler. You can easily check that \(W'W'x=x(W'W')\).

It should become

Using the second method, you should get the solution \(CL(CL)\), equivalent to the longer \(S,K,I\)-expression \(A_2A_2\) where \(A_2=S(K(SI))(S(KK)(SII))\).

Short explanation

The second method requires first to find a bird satisfying \(A_2yx=x(yy)\); either by the algorithm illustrated in Chapter 18 or by direct derivation, one finds the above result

\[ A_2 = CL = S(K(SI))(S(KK)(SII))\;, \]

leading to the right solution.

The expression given in the text does not fulfill the requirement: indeed,

\[ W'W'x = xW'W' \neq x(W'W') \]

because

\[ W'xy=yxx \neq y(xx)\, \]

where the parentheses are required if one is to honour the original expression given in the Problem of finding a bird \(A\) such that \(Ax=xA\) for any \(x\).