YES Confluence Proof

Confluence Proof

by csi

Input

The rewrite relation of the following TRS is considered.

+(x,y)

→

+(y,x)

Proof

1 Decreasing Diagrams

1.1 Relative Termination Proof

The duplicating rules (R) terminate relative to the other rules (S).

1.1.1 R is empty

There are no rules in the TRS R. Hence, R/S is relative terminating.

1.2 Rule Labeling

Confluence is proven, because all critical peaks can be joined decreasingly using the following rule labeling function (rules that are not shown have label 0).

+(x,y)→+(y,x) ↦ 0

There are no non-trivial critical pairs.

Tool configuration

csi

version: csi 1.2.5 [hg: unknown]
strategy: (if left-linear then (cr -dup;(( lpo -quasi || (matrix -dim 1 -ib 3 -ob 4 | matrix -dim 2 -ib 2 -ob 2 | matrix -dim 3 -ib 1 -ob 2 | arctic -dim 2 -ib 2 -ob 2) || (if duplicating then fail else (bounds -rt || bounds -rt -qc))[1] || poly -ib 2 -ob 4 -nl2 -heuristic 1 || fail )[5]*);shift -lstar);(rule_labeling | rule_labeling -left)?;decreasing else fail)!