A fine-grained parallel completion procedure

We present a parallel Knuth-Bendix completion algorithm where the inner loop, deriving the consequences of adding a new rule to the system, is multi-threaded. The selection of the best new rule in the outer loop, and hence the completion strategy, is exactly the same as for the sequential algorithm. Our implementation, which is within the PARSAC-2 parallel symbolic computation system, exhibits good parallel speedups on a standard multi-processor workstation.

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