Generators A_2: x y z;
Limiting weight: 10;
Relations:

[[x,y],x] - 2 x;
[[x,y],y] + 2 y;

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

[[x,z],z];
[[x,z],[x,[x,z]]] - 24 y.