Table 5.
Grammar for English (recursive) numeral system for the range 1–100.
NumberRuleComplexity
‘one’ $=d$1
‘two’ $=d$2
‘three’ $=d$3
‘four’ $=d$s (‘three’)
‘five’ $=d$s (‘four’)
‘six’ $=d$s (‘five’)
‘seven’ $=d$s (‘six’)
‘eight’ $=d$s (‘seven’)
‘nine’ $=d$s (‘eight’)
10 ‘ten’ $=d$s(‘nine’)
11 ‘eleven’ $=d$s (‘ten’)
12 ‘twelve’ $=d$s (‘eleven’)
13…19 u‘teen’ $=d$m (u) + m (‘ten’)
20…90 u‘ty’ $=d$m (u) × m (‘ten’)
21…99 u‘ty’-v $=d$m (u) × m (‘ten’) + m (v) 13
100 ‘hundred’ $=d$p (m (‘ten’), m (‘two’))
u ∈ {‘twen’, ‘thir’, …, ‘eigh’, ‘nine’} 10
v ∈ {‘one’, ‘two’, …, ‘eight’, ‘nine’} 11
‘twen’ ≡ ‘two’
‘thir’ ≡ ‘three’
‘for’ ≡ ‘four’
‘fif’ ≡ ‘five’
‘eigh’ ≡ ‘eight’
Σ = 117
NumberRuleComplexity
‘one’ $=d$1
‘two’ $=d$2
‘three’ $=d$3
‘four’ $=d$s (‘three’)
‘five’ $=d$s (‘four’)
‘six’ $=d$s (‘five’)
‘seven’ $=d$s (‘six’)
‘eight’ $=d$s (‘seven’)
‘nine’ $=d$s (‘eight’)
10 ‘ten’ $=d$s(‘nine’)
11 ‘eleven’ $=d$s (‘ten’)
12 ‘twelve’ $=d$s (‘eleven’)
13…19 u‘teen’ $=d$m (u) + m (‘ten’)
20…90 u‘ty’ $=d$m (u) × m (‘ten’)
21…99 u‘ty’-v $=d$m (u) × m (‘ten’) + m (v) 13
100 ‘hundred’ $=d$p (m (‘ten’), m (‘two’))
u ∈ {‘twen’, ‘thir’, …, ‘eigh’, ‘nine’} 10
v ∈ {‘one’, ‘two’, …, ‘eight’, ‘nine’} 11
‘twen’ ≡ ‘two’
‘thir’ ≡ ‘three’
‘for’ ≡ ‘four’
‘fif’ ≡ ‘five’
‘eigh’ ≡ ‘eight’
Σ = 117

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

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