In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed exchanges each give strongly normalizing rewrite strategies for connected string diagrams. We use this result to give a linear-time solution to the equivalence problem in the connected case, and a quadratic solution in the general case. We also give a stronger proof of the Joyal-Street coherence theorem, settling Selinger's conjecture on recumbent isotopy.

翻译：在平面字符串图的图形计算中,平等是由交换动作产生的,这些动作可以交换相邻的脊椎的高度。我们显示左手和右手的交换每个都为连接的字符串图提供了严格的正规化的重写策略。我们用这个结果来给连接的字符串图中的等同问题提供一个线性时间的解决方案,并在一般情况下提供一个二次式解决方案。我们还更有力地证明Joyal-Street一致性的定理,解决Selinger对复现的异构式的推测。