Finding flow decomposition

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In Daniel Marcus's Graph Theory - A Problem Oriented Approach:

According to the integral flow decomposition theorem, a flow with value n can be written as the sum of n unit path flows and possibly some cycle flows.

In problem 6, this theorem is supposed to apply in two different ways on the following flow:

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But I can only find the decomposition: UAB + AVC + 2(UABCV)

Have I misunderstood something?