Adding constants to string rewriting

René Thiemann*, Hans Zantema, Jürgen Giesl, Peter Schneider-Kamp

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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 symbols 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 investigate which properties are preserved by this transformation. It turns out that any TRS over a unary signature is terminating if and only if the corresponding 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.

Original languageEnglish
JournalApplicable Algebra in Engineering, Communications and Computing
Issue number1
Pages (from-to)27-38
Number of pages12
Publication statusPublished - 1. Feb 2008


  • Confluence
  • String rewriting
  • Term rewriting
  • Termination

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