```python
def estimate_region_lower_bound(region, var_dom, predicate):
    """Analyze the region with affine map, given the domain of variables and 
their predicate

    Parameters
    ----------
    region : List[Range]
        The region to be analyzed.

    var_dom : Dict[Var, Range]
        The ranges of the variables

    predicate : PrimExpr
        The predicate for the affine map

    Returns
    ----------
    region_int_set : Optional[List[IntSet]]
        None if the detection fails, or an array of IntSets as the result of 
analysis
    """
```

Perhaps this interface can help the purpose.





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