Abstract
Solving tangle equations is deeply connected with studying enzyme action on DNA. The main goal of this paper is to solve the system of tangle equations [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] are rational tangles, and [Formula: see text] is a 2-bridge link, for [Formula: see text], with [Formula: see text] and [Formula: see text] nontrivial. We solve this system of equations under the assumption [Formula: see text], the double branched cover of [Formula: see text], is not hyperbolic, i.e. [Formula: see text] is not [Formula: see text]-hyperbolic. Besides, we also deal with tangle equations involving 2-bridge links only under the assumption [Formula: see text] is an algebraic tangle.
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