... F(aa¯ a, aaaa) a ¯ ¯ A( a, a) F (a , aa) a ¯ A( a, a) D (a , aa) a ¯ E (a a, aaa) a ¯ ¯ D (a , aa) a ¯ C(ε, #) A (¯ , a) a ¯ D(ε, ε) F (a , aa) a ¯ A( a, a) D(ε, ε) E(¯ , a) a ¯ D(ε, ε) A (¯ , a) ... A, A , C, D, E, F}, Σ = {a, a, #}, and P consists of the following rules: S(x1 y1 , y2 x2 ) ← D(x1 , x2 ), C(y1 , y2 ) C(ε, #) ← S(aa¯ aa¯ , #¯ a aaa) a a a a D(aa¯ aa¯ , aa¯ aaa) a a ¯ a ... here a rigorous, mathematical proof of this fact not relying on the computer verification Head Grammars A head grammar is a quadruple G = (N, Σ, P, S), where N is a finite set of nonterminals, Σ is...