integralClosure

I think the following is messed up, but can't figure out why.
[Change QQ to ZZ/5 to see something which makes sense and should be a specialization of this.]
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R=QQ[f5,f3,g13,g12,MonomialOrder=>Lex];
I=ideal(f5^3+f5*f3+f3^5,f3^4-g12,f5^2*f3-g13);
G=gens gb I;
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R0=QQ[f13,f12,MonomialOrder=>{Weights=>{13,12},Weights=>{1,0}}];
phi=map(R0,R,matrix{{0,0,f13,f12}});
f=phi(G_(0,0));
I0=ideal(f);
A0=R0/I0;
icf=icFractions A0; toString icf
time G0=gens gb ideal integralClosure A0;
toString G0

The issue names no source files, tests, or entry points and provides only a Macaulay2 reproduction involving integralClosure, icFractions, and Groebner bases. Start by running the supplied transcript and tracing the integralClosure implementation; done means identifying and reproducing the discrepancy and establishing the expected result for the QQ and ZZ/5 cases.

Written by the indexing model from the issue text.