Generators A_5: x y z;P
Limiting weight: 34;
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]]]] - 768 y;
[z,[z,[x,z]]];
4 [[x,[x,[x,z]]],[z,[x,z]]] - 3 [[x,[x,z]],[z,[x,[x,z]]]] - 15552 z;
[[x,z],[[x,z],[[x,z],[[x,z],z]]]].