Return the exclusive endpoint of the maximal initial run:
PROCEDURE Run(a, b: INTEGER): INTEGER;
VAR c: INTEGER;
BEGIN
  IF a = b THEN RETURN b END;
  c := a+1;
  WHILE c < b DO
    IF u[c-1] > u[c] THEN RETURN c END;
    c := c+1
  END;
  RETURN c
END Run;
The loop invariant is and is nondecreasing. An unsuccessful adjacent-order test extends the run by one; a strict descent at prevents any extension across it. If , the whole segment is a run. The loop variant is .
(1)
For a run of length , the running time is , including at most one failed extension test; an empty segment takes .

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