It is believed that life passed through an RNA World stage in which replication was sustained by catalytic RNAs (ribozymes). The two most obvious types of ribozymes are a polymerase, which uses a neighbouring strand as a template to make a complementary sequence to the template, and a nucleotide synthetase, which synthesizes monomers for use by the polymerase. When a chemical source of monomers is available, the polymerase can survive on its own. When the chemical supply of monomers is too low, nucleotide production by the synthetase is essential and the two ribozymes can only survive when they are together. Here we consider a computational model to investigate conditions under which coexistence and cooperation of these two types of ribozymes is possible. The model considers six types of strands: the two functional sequences, the complementary strands to these sequences (which are required as templates), and non-functional mutants of the two sequences (which act as parasites). Strands are distributed on a two-dimensional lattice. Polymerases replicate strands on neighbouring sites and synthetases produce monomers that diffuse in the local neighbourhood. We show that coexistence of unlinked polymerases and synthetases is possible in this spatial model under conditions in which neither sequence could survive alone, hence, there is a selective force for increasing complexity. Coexistence is dependent on the relative lengths of the two functional strands, the strand diffusion rate, the monomer diffusion rate, and the rate of deleterious mutations. The sensitivity of this two-ribozyme system suggests that evolution of a system of many types of ribozymes would be difficult in a purely spatial model with unlinked genes. We therefore speculate that linkage of genes onto mini-chromosomes and encapsulation of strands in protocells would have been important fairly early in the history of life as a means of enabling more complex systems to evolve.