The bottom table is the computation time table of 15 benchmarks.

Benchmarks
  1. Example 6.4 of [VW1988]: Inputs & Logs

  2. Example 7 of [CM2014]: Inputs & Logs

  3. Example 8 of [CM2014]: Inputs & Logs

  4. Example 9 of [CM2014]: Inputs & Logs

  5. Example 5 of [FIS2015]: Inputs & Logs

  6. Example 6 of [FIS2015]: Inputs & Logs

  7. Example 7 of [FIS2015]: Inputs & Logs

  8. Example 8 of [FIS2015]: Inputs & Logs

  9. Example 9 of [FIS2015]: Inputs & Logs

  10. Example 10 of [FIS2015]: Inputs & Logs

  11. Example 1 of [FIS2016]: Inputs & Logs

  12. Example 2 of [FIS2016]: Inputs & Logs

  13. Example 3 of [FIS2016]: Inputs & Logs

  14. Example 4 of [FIS2016]: Inputs & Logs

  15. Example 5 of [FIS2016]: Inputs & Logs
Softwares
Remarks Computation Time Table

cgs syn rc res red rlh rl qep
01 0.287 0.167 120.741 0.054373 0.432344 N 0.03 6.374
02 1.153 N 2.145 0.098667 0.464517 N N E
03 0.987 0.537 29.931 0.262904 N 0.07 N N
04 105.810 111.379 2.020 0.055026 0.123643 59.82 N E
05 29.187 N N 31.054 N N N N
06 5.325 N N N N N E E
07 1.480 N N 274.349 274.894 247.68 N N
08 0.311 N N N 0.588577 N N N
09 564.126 17.481 N N N N N E
10 20.277 E E N N N N N
11 0.393 N 2.970 N N 1.479 N E
12 0.288 N N N N 1.529 N E
13 0.761 N N N N E N N
14 1.305 54.373 7.424 0.273433 1143.79 E 0.09 523.29
15 0.859 E N N N N N N


[CM2014] Chen, C. and Maza, M, M.:
Quantifier Elimination by Cylindrical Algebraic Decomposition Based on Regular Chains.
Proceedings of International Symposium on Symbolic and Algebraic Computation, pp. 91-98, ACM, 2014.

[FIS2015] Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato.:
Real Quantifier Elimination by Computation of Comprehensive Gröbner Systems.
Proceedings of the International Symposium on Symbolic and Algebraic Computation, pp. 173-180, ACM, 2015.

[FIS2016] Ryoya Fukasaku, Hidenao Iwane, Yosuke Sato.:
On the Implementation of CGS Real QE.
To appear in Proceedings of the International Congress on Mathematical Software, LNCS, Springer, 2016.

[VW1998] Weispfenning, V.:
A New Approach to Quantifier Elimination for Real Algebra.
Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 376-392, Springer, 1998.