A hypothetical way to compute an upper bound for the heights of solutions of a Diophantine equation with a finite number of solutions

Let f(n){2₂¹_n-2 if n=1 (2 + 2^2n-4)^2n-4 if nϵ [2, 3, 4, 5] if n ϵ [6, 7, 8 ....) We conjencturre that if a system T ⊆ {xi +1 = xk, xi = xk: i, j, k ϵ {l, ... ,n}} has only finitely many solutions in positive integers x1, ... , xn, then each such solution (x1, ... , xn) satisfies x1, ... , xn f(n). We prove that the function f cannot be decreased and the conjecture implies that there is an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite. We show that if the conjecture is true, then this can be partially confirmed by the execution of a brute-force algorithm.