# Rewritable Plain SO Tgds

Here we mainly provide additional experiments to the **Rewritable Plain SO Tgds** test (Section 5.4). The results show the change of rewriting rate with regard to the varying values of the rest four parameters of a plain SO tgd, which showed less influences compared to the parameters mentioned in the paper. If a parameter value is not explicitly given in the following figures, they are assigned the same values with the completeness test in the paper.

1. Below figure shows how the rewriting rate change with (a) the increasing number of source relation per part;(b) arity of source relations;(c) the increasing number of target relation per part;(b) arity of target relations. Here a plain SO tgd is rewritten to a set of nested tgds (i.e., a solution). In all four experiments we set number of Skolem function as 2.

We can see that these parameters have a relatively minor influence on rewriting rate. Note that in (c) by increasing the number of target relations, actually the number of Skolem function are also increasing. And we already know that the number of Skolem function has a significant impact on rewriting rate (Fig.7a in the paper).

2. For interested readers: below is how the rewriting rate change with the increasing number of source relation per part. Two subfigures are with different values of source relation arity. Here a plain SO tgd is rewritten to one nested tgd. We can obtain similar observations that number of source relations doesn't have a significant impact on rewritability, even with different rewriting strategies/artiy.

3. For testing the rewriting rate with increasing number of parts, we have set number of Skolem function as 2. This is because we have observed in this experiment numFuncs =1 setting has a different trend compared to the rest. This is because with only one Skolem Function per target relation (in this case, also per part). Thus there is no checks among multiple Skolem functions in a part. It just needs to be checked this single Skolem function of the part can satisfy the built LH-Skolem tree, which gives more possibilities for rewriting with the Relation mode. However, it doesn't suggest the general rule how number of Skolem function affects rewritability. We can observe that numFuncs =2, 3, 4... share a similar trend. Therefore in the paper Fig.7b for the experiment testing the impact of part numbers we included the results of Skolem function as 2. Here we provide full results for interested readers.