There is a standard way to convert a rewrite monoid into
a finitely presented monoid using the function Relations.
This is shown in the following example.
We construct the Fibonacci monoid FM(2, 4) as a rewrite monoid,
and then convert it into a finitely presented monoid.
> FM<a,b,c,d> := FreeMonoid(4);
> Q := quo< FM | a*b=c, b*c=d, c*d=a, d*a=b >;
> M := RWSMonoid(Q);
> Order(M);
11
> P<w,x,y,z> := quo < FM | Relations(M) >;
> P;
Finitely presented monoid
Relations
w * x = y
x * y = z
y * z = w
z * w = x
y^2 = w * z
z^2 = x * w
z * y = x^2
y * x = w^2
x * w * z = x^2
w^3 = w * z
x * w^2 = x * z
x^2 * z = x
w^2 * y = w
x^3 = x * w
x^2 * w = z
z * x = x * z
y * w = w * y
w^2 * z = y
x * w * y = x
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