In this task, you are given two sentences in the English language (Sentence 1 and Sentence 2). Your task is to identify the connecting word between the two sentences.

[Q]: Sentence 1:Such a restriction lowers the proof - theoretic strength of the system significantly . Sentence 2:For example , the system ACA described below is equiconsistent with Peano arithmetic .
[A]: for example


[Q]: Sentence 1:If verified , this would be the earliest known occupation of northern Europe by humans , as previous evidence had indicated that Europe was only sporadically occupied , at southerly latitudes , before 500,000 BP . Sentence 2:However , these findings have sparked a major controversy .
[A]: however


[Q]: Sentence 1:While the amphitheater 's capacity more than doubled , no known event warranted such an effort . Sentence 2:In fact , some evidence suggests that the population of Caesarodonum ( Tours ) had stopped growing by that time .
[A]:
in fact