Abstract-Let K be a two conjunctive normal form and φ a three conjunctive normal form, both formulas are defined over the same set of variables. It is well known that SAT(K) is in the complexity class P, while SAT(φ) is a classic NP-Complete problem. We consider the computational complexity of determining SAT(K φ ) as an incremental satisfiability problem (2-ISAT). We show that this problem is NP-complete even if the number of occurrences of each variable in φ is one.Also, we propose a method to review SAT(Kφ ). Our proposal is adequate to solve 2-ISAT problem. Our algorithm allows us to recognize tractable instances of 2-ISAT.