Report Number: CS-TR-74-417
Institution: Stanford University, Department of Computer Science
Title: Some thoughts on proving clean termination of programs.
Author: Sites, Richard L.
Date: May 1974
Abstract: Proof of clean termination is a useful sub-goal in the process of proving that a program is totally correct. Clean termination means that the program terminates (no infinite loops) and that it does so normally, without any execution-time semantic errors (integer overflow, use of undefined variables, subscript out of range, etc.). In contrast to proofs of correctness, proof of clean termination requires no extensive annotation of a program by a human user, but the proof says nothing about the results calculated by the program, just that whatever it does, it terminates cleanly. Two example proofs are given, of previously published programs: TREESORT3 by Robert Floyd, and SELECT by Ronald L. Rivest and Robert Floyd.
http://i.stanford.edu/pub/cstr/reports/cs/tr/74/417/CS-TR-74-417.pdf