for a, b being Element of INT st |.a.| > |.b.| & b > 1 holds
ex A, B being sequence of NAT ex C being Real_Sequence ex n being Element of NAT st
( A . 0 = |.a.| & B . 0 = |.b.| & ( for i being Nat holds
( A . (i + 1) = B . i & B . (i + 1) = (A . i) mod (B . i) ) ) & n = min* { i where i is Nat : B . i = 0 } & a gcd b = A . n & Fib (n + 1) <= |.b.| & n <= 5 * [/(log (10,|.b.|))\] & n <= C . |.b.| & C is polynomially-bounded )