Let G $=($V$,$ T$,$ S$,$ P$)$ be a phrase$-$structure grammar. Let w$0=$ lz$0$r and w$1=$ lz$1$r be strings over V$.$ If z$0->$ z$1$ is a production of G$,$ we say that w$1$ is

from w$0$ and we write w$0$ w$1.$ If w$0,$ w$1,$ w$2,...,$ wn are strings over V such that w$0$ w$1,$ w$1$ w$2,...,$ wn$1$ wn$,$ then we say that wn is

from w$0$ and we write w$0*$

wn$.$ The sequence of steps used to obtain wn from w$0$ is called a

$.$