Pathforms is an interactive game based on combinatorial group theory that visualizes Nielsen's algorithm for free groups of rank 1, rank 2 and of rank 3 on their Cayley graphs. Your goal is to apply Nielsen transformations to reduce the given paths to the Nielsen reduced form!
Rank 1 corresponds to a free group generated by a single element, for example S = {a}
Rank 2 corresponds to a free group generated by two elements: S = {a,b}
Rank 3 corresponds to a free group generated by three elements: S = {a,b,c}
Apply the dual transformations on generators S = {a,b}
Apply the dual transformations on generators S = {a,b,c}
Click on a rank to start exploring!
Go to Back and Forth the Nielsen Theorem for more information.