If ‘x’ is the sum ‘a + b’, then ‘nterms(
x)
’ must
be ‘nterms(
a)
’ plus ‘nterms(
b)
’. If ‘x’
is not a sum, then ‘nterms(
x)
’ = 1.
[ nterms(a + b) := nterms(a) + nterms(b), nterms(x) := 1 ]
Here we have taken advantage of the fact that earlier rules always match before later rules; ‘nterms(x)’ will only be tried if we already know that ‘x’ is not a sum.