We present a new constraint system called INES. Its constraints are conjunctions of inclusions t1 `t2 between first-order terms (without set operators) which are interpreted over non-empty sets of trees. The existing systems of set constraints can express INES constraints only if they include negation. Their satisfiability problem is NEXPTIME-complete. We present an incremental algorithm that solves the satisfiability problem of INES constraints in cubic time. We intend to apply INES constraints for type analysis for a concurrent constraint programming language.