------
## 最终结论
```python
def maxAbsValExpr(arr1, arr2):
    n = len(arr1)
    max_value = 0
    
    for sign1 in [1, -1]:
        for sign2 in [1, -1]:
            current_max = float('-inf')
            current_min = float('inf')
            for i in range(n):
                expression_value = sign1 * arr1[i] + sign2 * arr2[i] + i
                current_max = max(current_max, expression_value)
                current_min = min(current_min, expression_value)
            max_value = max(max_value, current_max - current_min)
    
    return max_value

# Example usage:
arr1_1 = [1, 2, 3, 4]
arr2_1 = [-1, 4, 5, 6]
print(maxAbsValExpr(arr1_1, arr2_1))  # Output: 13

arr1_2 = [1, -2, -5, 0, 10]
arr2_2 = [0, -2, -1, -7, -4]
print(maxAbsValExpr(arr1_2, arr2_2))  # Output: 20
```