The subtrace order and counting first order logic We study the subtrace relation among Mazurkiewicz traces which generalizes the much studied subword order. Here we consider the 2 variable fragment of a counting extension of first order logic with regular predicates. It is shown that all definable trace languages are effectively recognizable implying that validity of a sentence of this logic is decidable (this problem is known to be undecidable for virtually all stronger logics already for the subword relation).