I've identified an interesting semi-group in Australian slang ;)

(G, * )

G  = {yeah, nah}

Closure
yeah nah = nah
nah yeah = yeah
nah nah = nah
yeah yeah = yeah

Associativity
(yeah nah) yeah = yeah
yeah (nah yeah) = yeah

(yeah yeah) nah = nah
yeah (yeah nah) = nah

(nah yeah) nah = nah
nah (yeah nah) = nah

(nah nah) yeah = yeah
nah (nah yeah) = yeah

The above structure can be extended to a monoid, if we add the empty word as the identity element.