Many decision problem on security protocols can be reduced to solving so-called intruder constraints in the Dolev Yao model. Most constraint solving procedures for cryptographic protocol security rely on two properties of constraint systems called knowledge monotonicity and variable-origination. In this work we relax these restrictions by giving an NP decision procedure for solving general intruder constraints (that do not have these properties). Our result extends a first work by L. Mazaré in several directions: we allow non-atomic keys, and an associative, commutative and idempotent symbol (for modelling sets). We also discuss several new applications of our result.