Figure 2 shows how the positional joins work for our (expanded) motif from Table 4. At any stage in the process, the head symbol's pos-list corresponds to the full list of positions shown, whereas the tail's pos-list consists only of the positions shown in bold. For example, when computing A[1,4]CAT, the pos-list of the tail CAT is {2, 12, 15}, and that of the head symbol A is {3, 10, 13, 16}. Also, for illustration, we add a link between any two positions (x and y) in adjacent columns if their difference (d = y - x - 1) falls within the corresponding gap range. The joins begin with the last two symbols, with A as the head and T as the tail with a gap of [0,0]. The only positions x ∈ P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(A) that satisfy the adjacent gap constraint are 3, 13 and 16 (marked in bold), that form the pos-list of A[0,0]T. Next we join P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(C) with P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(A[0,0] T) to get the valid positions 2,12 and 15. At the next step we need to consider A as the head, with constraint [1,4], followed by the tail C [0,0] A [0,0] T. The only positions in P MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBamrtHrhAL1wy0L2yHvtyaeHbnfgDOvwBHrxAJfwnaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaWaaeGaeaaakeaacqqGqbauaaa@3786@(A) that satisfy the gap constraint of l = 1 and u = 4 are 10 and 13. Note also how position 2 that was in the tail's pos-list cannot be extended, since there is no position where A occurs within a gap of [1,4] before the tail CAT. The join process continues until the first symbol, and we finally get 5 as the only start occurrence for the full structured motif.