Pattern-matching notation (discard-upon-first-match)
$\delta(0,0,0) = 0$
$\delta(0,y,0) = \sup\{\delta(0,b,0)+1 \mid b < y\}$
$\delta(x,0,0) = \sup\{\delta(a,0,\omega) \mid a < x\}$
$\delta(x,y,0) = \sup\{\delta(a,\delta(a,b,\omega)+1,\omega) \mid a < x, b < y\}$
$\delta(x,y,z) = \sup\{\delta(x,\delta(x,y,c),0) \mid c < z\}$