### Table 5. Divide and conquer experiments.

2003

"... In PAGE 14: ... Changing the base order will greatly affect these numbers. Table5 shows the effect of the divide and conquer approach. For some exam- ples we observe a dramatic increase in performance whereas for other examples the required time increases significantly.... ..."

Cited by 25

### Table 10 Divide and conquer: termination.

"... In PAGE 27: ...55 all. In the nal table of this paper we present the individual timings for those examples in the collection of Arts and Giesl [3] for which the computation of at least one of the E and DP data in Table10 exceeds 5 seconds, together with [8, Example 11] (the di erentiation TRS of Example 25) and [23, Exam- ples 2.... ..."

### Table 3 Divide and conquer: quicksort (III).

"... In PAGE 20: ...3 Dynamic Programming The e ectiveness of the divide and conquer approach depends very much on the merge order. Table3 shows a di erent merge order for the rules of the quicksort example. Although the nal outcome is the same, the intermediate results di er greatly.... ..."

### Table 2. Divide and conquer, KBO, and other tools.

2003

"... In PAGE 7: ...11 (Quicksort) in [3], clearly reveals the benefits of the argument filtering heuristics as well as the new approach to cycle analysis. From columns (1), (2), and (3) in Table2 we infer that the divide and conquer option has an even bigger impact on this example, especially if one keeps in mind that all suitable argument filterings are computed. Here we used the new algorithm for cycle analysis, LPO with strict precedence as base order, EDG as dependency graph approximation, and some (1), some more (2), and all (3) argument filterings.... In PAGE 8: ... In contrast to the latter, TTT offers improved algorithms for the automatic search for suitable argument filterings. For the ARTS column in Table2 we used the only available automatic strategy in the distribution, which is (partly) described in [1, Section 3], and not guaranteed to terminate. Most of the successful termination proofs it generates use the refinements mentioned above.... ..."

Cited by 21

### Table 14: Divide and Conquer Computation of Tn(1)

1998

### Table 6.2: Divide and Conquer Algorithm

### Table 1. The divide-and-conquer coloring

"... In PAGE 2: ... Note that the colors used in supernodes 00 and 11 could be the same, but cannot be colors A and B. As an example, Table1 shows how this algorithm solves the coloring problem on dB(8, 2) recursively. A node v2v1 represented by the intersection of row v2 and column v1, and the symbol on the intersection is the color of that node.... ..."

### Table 1 Divide and conquer: quicksort (I).

"... In PAGE 18: ... The next example shows the e ectiveness of (restricted) partial argument l- terings. Example 37 Table1 shows for each rule l ! r the number of argument lterings in AF(Fun(l ! r)), AF(l ! r), AFvc(l ! r), and AFlpo(l ! r). The idea is now to (1) compute all argument lterings for each constraint separately and (2) subsequently merge them to obtain the argument lterings of the full set of constraints.... ..."