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More knowledge:
(0') forall m in N, n != 0: gcd(m, n) = gcd(m, m mod n)
Function definition (with recursion term m+n):
Euclid'(m, n) := if m = 0 then n else if n = 0 then m else if n <= m then Euclid'(m mod n, n) else Euclid'(m, n mod m)