Z3 Performance with Non-Linear Arithmetic

Question

We are running into performance problems with what I believe is the part of Z3 that treats non-linear arithmetic. Here is a simple concrete Boogie example, that when verifi

Answer 1

Yes, the non-termination is due to nonlinear integer arithmetic. Z3 has a new nonlinear solver, but it is for "nonlinear real arithmetic", and can only be used in quantifier free problems that only use arithmetic (i.e., no uninterpreted functions like in your example). Thus, the old arithmetic solver is used in your example. This solver has very limited support for integer arithmetic. Your analysis of the problem is correct. Z3 has trouble finding a solution for the block of nonlinear integer constraints. Note that if we replace f(100) * b == a * c with f(100) * b <= a * c, then Z3 returns immediately with an "unknown" answer.

We can avoid the non-termination by limiting the number of nonlinear arithmetic reasoning in Z3. The option NL_ARITH_ROUNDS=100 will use the nonlinear module at most 100 times for each Z3 query. This is not an ideal solution, but at least, we avoid the non-termination.