Rewriting modulo isotopies in Khovanov-Lauda-Rouquier's categorification of quantum groups

We study a presentation of the Khovanov - Lauda Rouquier's candidate 2-categorification quantum group using algebraic rewriting methods. use computational approach based on modulo isotopy axioms its pivotal structure to compute family linear bases for all vector spaces 2-cells this 2-category. show that these correspond and Lauda's conjectured generating sets, proving non-degeneracy their diagrammatic calculus. This implies 2-category is categorification Lusztig's idempotented integral Uq(g) associated with symmetrizable simply-laced Kac-Moody algebra g.