def test(wordLength, numTrials=10000):
    F.<a,b> = FreeGroup()
    W = FiniteWords('abAB')

    def letterToGroup(c):
        if c == 'a': return a
        if c == 'b': return b
        if c == 'A': return a^(-1)
        if c == 'B': return b^(-1)

    def wordToReln(w):
        return prod([letterToGroup(c) for c in w])

    numPerfect = 0
    numNontrivial = 0

    while numPerfect < numTrials:
        if numPerfect % 1000 == 0: print(numPerfect, "/", numTrials)
        R = W.random_element(length=wordLength)
        S = W.random_element(length=wordLength)

        # Check if the abelianization is trivial by checking
        # if the determinant of (R^ab | S^ab) is +/- 1
        det = (R.count('a') - R.count('A')) * (S.count('b') - S.count('B')) - \
               (R.count('b') - R.count('B')) * (S.count('a') - S.count('A'))

        if abs(det) == 1:
            numPerfect += 1

            G = F / [wordToReln(R), wordToReln(S)]

            # How can I make this line of code time out after 3 seconds
            # so we can move on to another random presentation?
            if G.cardinality() != 1:
                numNontrivial += 1

    return (numNontrivial / numPerfect).n()