 
Summary: To appear in Applicable Algebra in Engineering,
Communication and Computing
Ren’e Thiemann · Hans Zantema ·
J˜urgen Giesl · Peter SchneiderKamp
Adding Constants to String Rewriting
Abstract We consider unary term rewriting, i.e., term rewriting with unary
signatures where all function symbols are either unary or constants. Terms
over such signatures can be transformed into strings by just reading all sym
bols in the term from left to right, ignoring the optional variable. By lifting
this transformation to rewrite rules, any unary term rewrite system (TRS)
is transformed into a corresponding string rewrite system (SRS). We investi
gate which properties are preserved by this transformation. It turns out that
any TRS over a unary signature is terminating if and only if the correspond
ing SRS is terminating. In this way tools for proving termination of string
rewriting can be applied for proving termination of unary TRSs. For other
rewriting properties including confluence, unique normal form property, weak
normalization and relative termination, we show that a similar corresponding
preservation property does not hold.
Keywords term rewriting · string rewriting · termination · confluence
1 Introduction
