Most General Unifiers

A unifier S1 for L1 and L2 is a most general unifier (MGU) for L1 and L2 provided that for any other unifier S2 of L1 and L2 there exists a substitution S3 such that

S3(S1(L1)) = S2(L1).

S1 = { y/x } is a most general unifier for P(x), P(y).

S2 = { f(a)/x, f(a)/y } is not a MGU for P(x), P(y).

S3 = { f(a)/y }

S3(S1(P(x))) = P(f(a)) = S2(P(x)).

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