Solving First-Order Constraints in the Theory of the Evaluated Trees
Résumé
We describe in this paper a general algorithm for solving first-order constraints in the theory T of the evaluated trees which is a combination of the theory of finite or infinite trees and the theory of the rational numbers with addition, subtraction and a linear dense order relation. It transforms a first-order formula ϕ, which can possibly contain free variables, into a disjunction φ of solved formulas which is equivalent in T, without new free variables and such that φ is either $\mathit{true}$ or $\mathit{false}$ or a formula having at least one free variable and being equivalent neither to $\mathit{true}$ nor to $\mathit{false}$ in T.
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