RPO Constraint Solving Is in NP

A new decision procedure for the existential fragment of ordering constraints expressed using the recursive path ordering is presented. This procedure is nondeterministic and checks whether a set of constraints is solvable over the given signature, i.e., the signature over which the terms in the constraints are defined. It is shown that this non-deterministic procedure runs in polynomial time, thus establishing the membership of this problem in the complexity class NP for the first time.

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