On the Tits alternative for cyclically presented groups with length four positive relators

We investigate the Tits alternative for cyclically presented groups with length four positive relators in terms of a system of congruences (A),(B),(C) in the defining parameters, introduced by Bogley and Parker. Except for the case when (B) holds and neither (A) nor (C) hold, we show that the Tits alternative is satisfied; in the remaining case we show that the Tits alternative is satisfied when the number of generators of the cyclic presentation is at most 20