There exists a mapping p of P(w) such that q = p |I . Thus there exists an ancestor w c = w(v ic , t , I J , S ) of w in S(I) and a mapping p c of P(w c ) such that p c generates p. Let anc(q) = p c|I . If |P(w, I)| > |A|, there exist two mappings q 1 and q 2 in P(w, I) such that anc(q 1 ) = anc(q 2 ) ,

,

, We assume capa is fixed and want to prove that the algorithm is polynomial in |I| and T W . Note firstly that S(I) has |S(I)| = O(n · T W · n capa · n) nodes, thus Line 1 is done in time at most O(|S(I)| 2 ) = O(T W 2 · n 2·capa+4 )

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