Simultaneous critical pairs and Church-Rosser property

Decreasing Diagrams and Relative Termination

“…[15,24,26]) can be used for this purpose. The idea here is to exclude the critical pair steps that give rise to critical pairs whose joinability can be shown by the conditions of the considered criterion.…”

“…[15,24,26,31]), and divide and conquer techniques based on persistence [2], layer-preservation [22], and commutativity [29]. The latest version of ACP [1] also supports the rule-labeling heuristic for the original version of decreasing diagrams (cf.…”

Generalizing Newman’s Lemma for Left-Linear Rewrite Systems

“…in particular those of [26], [11], [8], [23], [24], [21], [7], [6] it turns out to be incomparable w.r.t. all of them.…”

“…e.g. [26], [11], [27], [29], [8], [23], [24], [21]). Known related decidability results include [7], [6].…”

“…Even though these critical pairs are joinable (cf. the reduction graphs), none of the critical pair based confluence criteria for left-linear rewrite systems in [11,8,23,24,21] is applicable here. Also, decidability results of [7], [6] are not applicable.…”