# changed FAIL to "FAIL"
with(LinearAlgebra, Transpose):	
findgauge := proc(Ra,Rb,u,v,n) # Input: Ra fn of u, Rb fn of v. Output Ra = a0*Rb(n) + a1*Rb(n+1) i.e. finds GT Rb->Ra (applygauge finds GT input1->output)
local s,g,A,Y,d,ShouldBeZero,sols,solbo,solbe,r0,r1,i;
# option trace;
s := u(n) = r0(n)*v(n) + r1(n)*v(n+1);
ShouldBeZero := eval(Ra, {s, subs(n=n+1, s), subs(n=n+2, s)});
solve(Rb, v(n+2));
solve( eval(Rb, n=n+1), v(n+3));
subs(v(n+3)=%, v(n+2) = %%, ShouldBeZero);
collect(%, {v(n), v(n+1)}, factor);
ShouldBeZero := { coeffs(%, {v(n),v(n+1)}) };
d:=solve(ShouldBeZero, {r0(n+2), r1(n+2)});
assign(d);
Y := [r0(n), r0(n+1), r1(n), r1(n+1)];
#ShiftY := [r0(n+1), r0(n+2), r1(n+1), r1(n+2)];
# A := <<0|1|0|0>, Transpose(<seq(coeff(r0(n+2),i),i in Y)>), <0|0|0|1>, Transpose(<seq(coeff(r2(n+2),i),i in Y)>)>;
A := <<0|1|0|0>, Transpose(<seq(coeff(r0(n+2),i),i in Y)>), <0|0|0|1>, Transpose(<seq(coeff(r1(n+2),i),i in Y)>)>;
Y := LinearFunctionalSystems[RationalSolution](A,n,'difference');
if not({op(Y)} in {{},{0}}) then
 s:=subs({r0(n)=Y[1], r1(n)=Y[3]}, s);
else "FAIL"
fi
end: