detect coverings

[videlec]

There is a general covering construction for iet that works as follows

1. Pick an iet T1: I → I with labels A = {a, b, c, ...}, a positive integer n, a function f: A → Sym({1, 2, ..., n}) and an admissible subinterval J ⊂ I
2. Consider the skew product T2: I x {1, 2, ..., n} → I x {1, 2, ..., n} defined as T2(x, i) = (T x, s(x)(i)) where we abused notation s(x) = s(label of the subinterval to which x belongs). This function T2 is an iet on a disjoint union of n intervals.
3. Now let T3 be the first return map of T2 on J x {1}. Then T3 is an iet in the standard sense.

The algorithmic question is: Given T3 can we check whether there exists a construction as above (ie T1, n, f and J)? Without such algorithm, #86 could only be solved in the primitive situation.