AC-3是否解决了路径一致性问题？

Question

当我读到AC-3 in Artificial Intelligence: A Modern Approach的伪代码时，我认为它解决了路径一致性和弧一致性问题。但书中说，路径一致性是由PC-2算法解决的。我错过了什么吗？

为什么AC-3不足以解决路径一致性问题？

下面是AC-3的代码

function AC-3(csp) returns false if an inconsistency is found and true otherwise 
    inputs: csp, a binary CSP with components (X, D, C)
    local variables: queue, a queue of arcs, initially all the arcs in csp

    while queue is not empty do
        (Xi, Xj)←REMOVE-FIRST(queue) 
        if REVISE(csp, Xi, Xj) then
            if size of Di = 0 then return false
            for each Xk in Xi.NEIGHBORS - {Xj} do
                add (Xk, Xi) to queue 
    return true

function REVISE(csp, Xi, Xj) returns true iff we revise the domain of Xi 
    revised ← false
    for each x in Di do
        if no value y in Dj allows (x,y) to satisfy the constraint between Xi and Xj then 
            delete x from Di
            revised ← true
    return revised

提前感谢：)