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R is orthogonal iff it is non-overlapping and left-linear

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• R is non-overlapping iff it does not have any critical pairs.

• R is left-linear iff its left-hand sides do not contain multiple occurrences of the same variable.

• R is orthogonal iff it is non-overlapping and left-linear.

• Strong Confluence p s

=

t q =

implies confluence (Thm. 5.3.6)

• Parallel Reduction Relation: s ⇒R t iff there exist

– a set Π = {π1, . . . , πn} of pairwise independent positions of s – rules li → ri ∈ R

– substitutions σi

with s|πi = liσi and t = s[r1σ1]π1 . . . [rnσn]πn.

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