Finding simple sequence from reads with significant overlap
Miniasm will probably work for this; it's designed to be an ultra-fast, greedy assembler, which has been used for people doing real-time assemblies from MinION data. Because of its greedy nature, it can misassemble regions where the overlapping fragments are ambiguous, so it's worth using some other method in addition to miniasm to confirm that the assembly is correct.
By default it looks for overlap regions that have a coverage of 3 reads when joining (option -c), but I assume that could be reduced down to 2 reads, as in your example (which has a minimum overlapping coverage of 2).