// ------------------- INITIALIZATION -------------------
P := zero matrix of size Q x V^2        // Visited configurations
M := zero matrix of size Q x V^2        // Current frontier

for each nonterminal i do
    graph_nt[i] := zero matrix of size V x V

// Seed initial frontier and visited
q_start = start_states[start_nonterm]
for each start_vertex in sources do
    diag_col := start_vertex * V + start_vertex
    M[q, diag_col] := true
    P[q, diag_col] := true

// ------------------- MAIN FIXED-POINT LOOP -------------------
while M is not empty do

    // Phase 1: TERMINAL TRANSITIONS
    M_term := zero matrix Q x V^2
    for each terminal a do
        M_term |= rsm_term[a]^T @ M @ graph_term[a]

    // Phase 2: NONTERMINAL TRANSITIONS
    M_nonterm := zero matrix Q x V^2
    for each nonterminal i do
        M_nonterm |= rsm_nonterm[i] @ M @ graph_nt[i]

    // Phase 3: CALL TRANSITIONS
    M_call := zero matrix Q x V^2
    for each nonterminal i do
        mask_call := rsm.call[i]^T @ M
        mask_call := reshape(mask_call, Q*V x V)
        entry_vec := column_OR(mask_call)  // Boolean vector of size V
        diag_entry := diag(entry_vec) // VxV
        diag_entry := reshape(diag_entry, 1 x V^2)
        outer_result := rsm_start[i] @ diag_entry  // |Q|x1 @ 1x|V^2| -> |Q|x|V^2|
        M_call |= outer_result

    // Phase 4: RETURN TRANSITIONS
    M_return := zero matrix Q x V^2
    for each nonterminal i do
        // Collect new completed edges for this nonterminal
        new_edges := final_states[i] @ M            // 1x|Q| @ |Q|x|V^2| -> 1x|V^2|
        new_edges := reshape(new_edges, V x V)
        graph_nt[i] |= new_edges
        
        // Restore callers from stack and advance them
        M_return |= rsm_nonterm[i]^T @ P @ new_edges

    // Phase 5: MERGE & MARK VISITED
    M_new := (M_term | M_nonterm | M_call | M_return) & ~P
    P |= M_new
    M := M_new

end while

// ------------------- RESULT -------------------
return row start_vertex of graph_nt[start_nonterm]