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# is any valid expression

WEAK{#n,m#} = WEAK{#n+m#}

WEAK{#n(x)m#} WEAK{#n(x-1)n(x-1)n(x-1)...n(x-1)n(x-1)n(x-1)n#} with m n(x-1)n's

WEAK{#(1)#} = WEAK{#,#}

WEAK{n} = n

-- UNDER CONSTRUCTION --

Rest of rules apply as normal BEAF.

FGH

Weak BEAF FGH Ordinal
WEAK{n,m} 1
WEAK{n(2)m} 2
WEAK{n(3)m} 3
WEAK{n(4)m} 4
WEAK{n(x)m} \omega
WEAK{WEAK{X(4)X}&n}, since & operator works inside WEAK{} \omega+1
WEAK{WEAK{X(5)X}&n} \omega+2
WEAK{WEAK{X(m)X}&n} \omega2
WEAK{WEAK{WEAK{X2(4)X2}&X}&n}, Xis to X as X is to n. \omega2+1

-- UNDER CONSTRUCTION --

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