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Let $K_1, K_2$ be two knots with $t(K_1)+t(K_2)>2$ and $t(K_1 # K_2)=2$.Then, in the present paper, we will show that any genus three Heegaardsplittings of $E(K_1 # K_2)$ is strongly irreducible and that $E(K_1 # K_2)$has at most four genus three Heegaard splittings up to homeomorphism. Moreover,we will give a complete classification of those four genus three Heegaardsplittings and show unknotting tunnel systems of knots $K_1 # K_2$corresponding to those Heegaard splittings.

On Heegaard splittings of knot exteriors with tunnel number degenerations