Generators: x_1 x_2 -y;
Parameters, inf. b = 1, c = 3: b c;
Relations:

[[[y,x_1],x_1],x_1];
[y,x_2];
[y,[[[y,x_1],x_1],y]];
[y,[[y,x_1],[y,x_1]]] - 2 [[y,[[y,x_1],y]],x_1];

b [x_1,x_2] - [[y,[[y,[[y,x_1],y]],y]],y];
[x_1,[[y,x_1],y]] + [[y,x_1],[y,x_1]] + [[[y,x_1],x_1],y];
[x_1,[[y,x_1],[y,x_1]]] + [x_1,[[[y,x_1],x_1],y]];
[x_1,[[y,[[y,x_1],y]],y]] - c [[y,x_1],y] - [[[y,[[y,x_1],y]],x_1],y];