GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Generators: X Y T; Weights: 1 1 1; Limiting weight: 6; Parameters: c_1 c_3 c_4 c_5; Relations: [[Y,X],Y] + c_5 Y; [[Y,X],X] + c_1 [Y, X] + [T,Y] + c_4 Y; [T,X] + c_3 Y;