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For me it looks like a bug to me. However it seems to work as follows (the example in the documentation uses it)

sage:  R.<x,y> = FreeAlgebra(QQ, implementation='letterplace')
sage: I = R*[x*y-y*x]*R
sage: Q.<a,b> = R.quo(I)
sage: a*b
b*a
sage: a*a*b == a*b*a == b*a*a
True
sage: Q.is_commutative()

For me it It looks like a bug to me. However it seems to work as follows (the example in the documentation uses it)

sage:  R.<x,y> = FreeAlgebra(QQ, implementation='letterplace')
sage: I = R*[x*y-y*x]*R
sage: Q.<a,b> = R.quo(I)
sage: a*b
b*a
sage: a*a*b == a*b*a == b*a*a
True
sage: Q.is_commutative()
True