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i have a reduce operation which includes Fibonacci function. but the problem is it never terminates, i tried some modifications, for example removing f1 in my relation. sometimes it works and at least it gives me an output. but the relation itself MUST NOT change and i dont want to modify the expressions. Could you help me what the problem is, seems it is a loop or something? This expression cause the problem f1*Fibonacci[1 + j - N], also f1*Fibonacci[j - N]]].

NONE of the expressions must change, every single expression is needed and no add/remove/modification is allowed

Reduce[Exists[{i, f, j, f1, f2, N}, 
  i == iPP && f == fPP && j == jPP && f1 == f1PP && f2 == f2PP && 
   N == NPP && j >= N && iP == i + j - N && jP == N && 
   f1P == f2* Fibonacci[j - N] + f1*Fibonacci[1 + j - N] &&   
   f2P == f2 *Fibonacci[-1 + j - N] + f1*Fibonacci[j - N]]]
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    $\begingroup$ Reduce has the form: Reduce[expr, variables]. You do not specify any variables. $\endgroup$ Jan 14 at 16:06
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    $\begingroup$ N has a predefined meaning in Mathematica and should not be used as a user-defined symbol. $\endgroup$
    – Bob Hanlon
    Jan 14 at 16:17
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thanks to @DanielHuber, I found the issue.

Reduce[Exists[{i, f, j, f1, f2, N}, 
  i == iPP && f == fPP && j == jPP && f1 == f1PP && f2 == f2PP && 
   N == NPP && j >= N && iP == i + j - N && jP == N && 
   f1P == f2* Fibonacci[j - N] + f1*Fibonacci[1 + j - N] && 
   f2P == f2 *Fibonacci[-1 + j - N] + f1*Fibonacci[j - N]] , {fP, f1P,
   f2P, iP, jP}, Reals, Backsubstitution -> True]
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