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...plementation and report on experimental data. 10 5.1 Implementation In order to automate Theorem 2 we employed TTT2 v1.06 [17] for checking relative termination R/S and an extended version of Maxcomp =-=[14]-=- for testing S-unifiability, using ordered completion. To check confluence of S, we used the existing three state-of-the-art confluence provers: ACP v0.20 [3]2, CSI v0.1 [27]3, and Saigawa v1.2 [10]4....

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...Ss and MKBTT 80 ESs while both tools together succeeded on 94. The corresponding 94 completion proofs could be certified by CeTA (version 2.4). For an evaluation of other completion tools we refer to =-=[4]-=-. In our experiments we considered both possibilities (mentioned at the end of Section 2) to ensure ↔∗R ⊆ ↔∗E . While KBCV 1.6 performs the recall phase to explicitly construct `↔∗E r for each `→ r ∈ ...

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...ariant of the above inference system and then commit to a specific strategy to implement a completion procedure. There are several such tools available today, e.g., Slothrop [23], MKBTT [18], Maxcomp =-=[11]-=-, and KBCV [21]. One of the main issues was that most of these tools have not been designed to handle problems with a magnitude counting thousands of equations. In the end we decided to use KBCV for s...