Procedure.

ComputeNumSolutions(G, S, , P_Σ, P_Δ, P_Θ)

1: for each and do

2:   Initialize c(g, s), cΣ(g, s), cΔ(g, s), and cΘ(g, s) to ∞, and N(g, s) to 0.

3: for each do

4:   Initialize c(g, (g)) to 0, and N(g, (g)) to 1.

5: for each in post-order do

6:   for each in post-order do

7:    Let {g′, g″} = ChG(g).

8:     ifthen

9:   cΣ(g, s) = ∞.

10:   cΔ(g, s) = PΔ + c(g′, s) + c(g″, s).

11:   cΘ(g, s) = PΘ + min{in(g′, s) + out(g″, s), in(g″, s) + out(g′, s)}.

12:   c(g, s) = min{cΣ(g, s), cΔ(g, s), cΘ(g, s)}.

13:   Assign the three ai expressions as described earlier (for the case when and, for each , compute N(ai) using Equation 2.

14:   Compute N(g, s) using Equation 3.

15:  else

16:   Let {s′, s″} = ChS(s).

17:   cΣ(g, s) = min{in(g′, s′) + in(g″, s″), in(g″, s′) + in(g′, s″)}.

18:

19:   If s ≠ rt(S), then cΘ(g, s) = PΘ + min{in(g′, s) + out(g″, s), in(g″, s) + out(g′, s)}.

20:   c(g, s) = min{cΣ(g, s), cΔ(g, s), cΘ(g, s)}.

21:   ifs ≠ rt(S) then

22:    Assign the thirteen ai expressions as described earlier (for the case when and compute N(ai), for each , using Equation 2.

23:    Compute N(g, s) using Equation 1.

24:   ifs = rt(S) then

25:    Assign the eleven ai expressions as described earlier (for the case when s = rt(S)) and compute N(ai), for each , using Equation 2.

26:    Compute N(g, s) using Equation 4.