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Scott's conjecture is true, position sensitive weights



The classification of total reduction orderings for strings over a 2-letter alphabet w.r.t. monoid presentations with 2 generators was published by U. Martin, see [9], and used the hypothetical truth of Scott's conjecture, which was 3 years old in 1996. Now the results due to Ursula Martin and Elizabeth Scott are completed with the truth of Scott's conjecture. The final proof is simple, but we had difficulties. E. Scott proved the case, when some invariant takes the value either 0, or a positive rational or infinity, see [15]. Later we proved the case of positive reals which are well approximable to arbitrary order, see [11], and then the case of (n) root k and the case of lambda where both of lambda and lambda(-1) are algebraic integers, like root 5 - 1 / 2 It is a challenging problem, whether there is a reasonably small subset G subset of or equal to {a, b}* x {a, b}* such that each total reduction ordering > of {a, b}* is uniquely determined by its restriction to G

Topics: QA76
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