Generators A_3: x y z;
Limiting weight: 18;
Relations:

[[x,y],x] - 2 x;
[[x,y],y] + 2 y;

[y,z];
[[x,y],z] + 4 z;
[x,[x,[x,[x,[x,z]]]]];

3 [[x,z],[x,[x,z]]] - 2 [z,[x,[x,[x,z]]]] - 288 y;
[z,[z,[x,z]]];
[[x,[x,[x,z]]],[z,[x,z]]] - 576 z;
[[x,z],[[x,z],z]];