FpGroup.make_confluent produces buggy rewrites

[boothby]

In sympy version 1.11.1:

from sympy.combinatorics.free_groups import free_group
from sympy.combinatorics.fp_groups import FpGroup

G0, x = free_group('x')
G = FpGroup(G0, [x**4])
assert G.equals(x**4, G.identity) #True
G.make_confluent()
assert G.equals(x**4, G.identity) #False?!

Digging a little: before make_confluent is called, we have G.reduce(x**4) = <identity>. Afterwards, we have G.reduce(x**4) = x**-4.

[oscarbenjamin]

I don't know much about this topic or this part of the codebase but does the comment or code here shed any light: https://github.com/sympy/sympy/blob/f3805d0e5bd2d718f1b6b6f680cb5065586c083f/sympy/combinatorics/fp_groups.py#L101-L114

[boothby]

It does. It says that misleading output may occur before make_confluent is called but not after. What I'm observing is the opposite.

[oscarbenjamin]

Is the output of self.reduce(word1*word2**-1) correct (before or after)?