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We give an algorithm for deciding E-uni cation problems for linear standard equational theories (linear equations with all shared variables at a depth less than two) and varity 1 goals (linear equations with no shared variables). We show that the algorithm halts in quadratic time for the non-uniform E-uni cation problem, and linear time if the equational theory is varity 1. The algorithm is still polynomial for the uniform problem. The size of the complete set of uni ers is exponential, butdoi:10.1007/3-540-45653-8_13 dblp:conf/lpar/LynchM01 fatcat:c35aonbymja5palllxr7jgkdly