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Table 5.

Grammar for English (recursive) numeral system for the range 1–100.

Number	Rule	Complexity
1	‘one’ $\overset{d}{=}$ 1	3
2	‘two’ $\overset{d}{=}$ 2	3
3	‘three’ $\overset{d}{=}$ 3	3
4	‘four’ $\overset{d}{=}$ s (‘three’)	4
5	‘five’ $\overset{d}{=}$ s (‘four’)	4
6	‘six’ $\overset{d}{=}$ s (‘five’)	4
7	‘seven’ $\overset{d}{=}$ s (‘six’)	4
8	‘eight’ $\overset{d}{=}$ s (‘seven’)	4
9	‘nine’ $\overset{d}{=}$ s (‘eight’)	4
10	‘ten’ $\overset{d}{=}$ s(‘nine’)	4
11	‘eleven’ $\overset{d}{=}$ s (‘ten’)	4
12	‘twelve’ $\overset{d}{=}$ s (‘eleven’)	4
13…19	u‘teen’ $\overset{d}{=}$ m (u) + m (‘ten’)	8
20…90	u‘ty’ $\overset{d}{=}$ m (u) × m (‘ten’)	8
21…99	u‘ty’-v $\overset{d}{=}$ m (u) × m (‘ten’) + m (v)	13
100	‘hundred’ $\overset{d}{=}$ p (m (‘ten’), m (‘two’))	7
	u ∈ {‘twen’, ‘thir’, …, ‘eigh’, ‘nine’}	10
	v ∈ {‘one’, ‘two’, …, ‘eight’, ‘nine’}	11
	‘twen’ ≡ ‘two’	3
	‘thir’ ≡ ‘three’	3
	‘for’ ≡ ‘four’	3
	‘fif’ ≡ ‘five’	3
	‘eigh’ ≡ ‘eight’	3
		Σ = 117

Number	Rule	Complexity
1	‘one’ $\overset{d}{=}$ 1	3
2	‘two’ $\overset{d}{=}$ 2	3
3	‘three’ $\overset{d}{=}$ 3	3
4	‘four’ $\overset{d}{=}$ s (‘three’)	4
5	‘five’ $\overset{d}{=}$ s (‘four’)	4
6	‘six’ $\overset{d}{=}$ s (‘five’)	4
7	‘seven’ $\overset{d}{=}$ s (‘six’)	4
8	‘eight’ $\overset{d}{=}$ s (‘seven’)	4
9	‘nine’ $\overset{d}{=}$ s (‘eight’)	4
10	‘ten’ $\overset{d}{=}$ s(‘nine’)	4
11	‘eleven’ $\overset{d}{=}$ s (‘ten’)	4
12	‘twelve’ $\overset{d}{=}$ s (‘eleven’)	4
13…19	u‘teen’ $\overset{d}{=}$ m (u) + m (‘ten’)	8
20…90	u‘ty’ $\overset{d}{=}$ m (u) × m (‘ten’)	8
21…99	u‘ty’-v $\overset{d}{=}$ m (u) × m (‘ten’) + m (v)	13
100	‘hundred’ $\overset{d}{=}$ p (m (‘ten’), m (‘two’))	7
	u ∈ {‘twen’, ‘thir’, …, ‘eigh’, ‘nine’}	10
	v ∈ {‘one’, ‘two’, …, ‘eight’, ‘nine’}	11
	‘twen’ ≡ ‘two’	3
	‘thir’ ≡ ‘three’	3
	‘for’ ≡ ‘four’	3
	‘fif’ ≡ ‘five’	3
	‘eigh’ ≡ ‘eight’	3
		Σ = 117

Note. Each rule is composed of symbols, and each symbol adds a unit complexity of 1.