Russian Academy of Sciences
Abstract:
We prove an upper bound on the heights of terms occurring in a most general unifier of a system of pairs of terms in case when unknowns are divided to two types. An unknown belongs to the first type if all occurrences of this unknown have the same depth, we call such unknown an unknown of the cut type. Unknowns of the second type (unknowns of not the cut type) are unknowns that have arbitrary occurrences. We bound from above the heights of terms occurring in a most general unifier in terms of the number of unknowns of not the cut type and the height of the system. This bound yields an upper bound on the sizes of proofs in the Gentzen sequent calculus LK. Namely, we show that one can transform a proof D in LK by substituting some free terms in places of variables in such a way that the heights of terms occurring in the proof may be bounded from above by ar [D] hc \Delta q
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