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Identity in a quotient Group

Hello everyone, I have the following groups

F3.<a1,b1,a2,b2,a3,b3> = FreeGroup()
H3 = F3.quotient([a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3])


Then I inject the variables to $H3$

H3.inject_variables()


Now when every element that I write have parent $H3$, but when I write the word a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3 this does not return the identity of $H3$, although if I put

a1*b1/a1/b1*a2*b2/a2/b2*a3*b3/a3/b3 == H3.one()


this is true. Does anyone know why this happen and how can I get sage to reduce this word to identity of $H3$?