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  "body": "\n## Definition\n\nLet $\\sigma$ be a signature with only function symbols, let $X$ be a set of variables, and let $s, t$ be [[terms|6D3WA7N2W4]] over $\\sigma$ and $X$.\nA *unifier* of $s$ and $t$ is a [[substitution|NCDZ969V7X]] $\\theta$ with $s\\theta = t\\theta$, equality meaning identical terms.\nA unifier $\\theta$ is a *most general unifier* if the following holds for every unifier $\\eta$ of $s$ and $t$.\nThere is a substitution $\\rho$ with $x\\eta = (x\\theta)\\rho$ for every variable $x$.\n*Unification* is the problem of deciding whether two given terms have a unifier and of finding a most general one.\n\n## Remarks\n\nIf $s$ and $t$ have a unifier, then they have a most general unifier, unique up to renaming of variables, and Robinson's algorithm finds it.\nThe same notions apply to finite sets of pairs of terms, which are unified simultaneously.\nIn $E$-unification one asks instead for $s\\theta \\approx t\\theta$ to follow from a set $E$ of identities.\n\nExample: $s = f(x, b)$ and $t = f(a, y)$, with constants $a, b$, have the unifier $\\theta = \\set{x \\mapsto a, \\ y \\mapsto b}$.\nIndeed $s\\theta = f(a, b) = t\\theta$, and $\\theta$ is most general because every unifier must send $x$ to $a$ and $y$ to $b$.\n\nNon-example: $x$ and $f(x)$ have no unifier.\nFor every substitution $\\theta$, the term $f(x)\\theta = f(x\\theta)$ has one more symbol than $x\\theta$, so they are never identical.\n",
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