Backtrack Search Algorithm Using Shortened Base Images Input: a group G with a basis B=[131,132...... 13k] and a strong generating set S; a decidable property P, the members of which form a subgroup; Output: a strong generating set relative to B for the subgroup K = H (P) ; procedure search(G: group; P: property; s: 1..k+l; 1: 1..k+l; varK: group); (* Search G (s) for elements fulfilling P in the subgroup K. The components of G (0 are known to fulfil P. *)

Backtrack Search Algorithm Using Shortened Base Images
Input: a group G with a basis B=[131,132...... 13k] and a strong generating set S; a decidable property P, the members of which form a subgroup;
Output: a strong generating set relative to B for the subgroup K = H (P) ; procedure search(G: group; P: property; s: 1..k+l; 1: 1..k+l; varK: group); (* Search G (s) for elements fulfilling P in the subgroup K.
The components of G (0 are known to fulfil P. *)