Abstract
A loop of a semi-Thue system is a reduction chain where the start word reappears as a factor of the obtained word after a finite number of reduction steps. A rewriting system admitting a loop is clearly nonterminating. The semi-Thue systems consisting of only one rule which admit loops of length 1, 2 or 3 are characterized. Length-1-loops are trivial. 2-loops turn out to have a unique structure, whereas one-rule systems admitting a 3-loop (but no 2-loop) can belong to three structurally different types.
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