…parameter

…acking.

- Introduce `set_debug_level!` for configurable debug options. - Update functions to include `SearchStatistics` for better performance analysis.

…sult` structure.

- Include `twosat.jl` in the Boolean inference module.
- Refactor branching functions to return `BranchResult` for improved clarity and performance.
- Update debug logging to utilize the new `@dbg` macro for better control over logging levels.

…return values in branching functions.

- Rename `vec2tensor` to `vec_to_tensor` and `lluint2vec` to `longlonguint_to_vec` for better readability.
- Update corresponding function calls and tests to reflect the new names.
- Improve comments for better understanding of the code logic.

…function.

- Add detailed debug logging for branching attempts, including propagated variables and remaining constraints.
- Refactor `deduction_reduce` to use `append!` for modifying the reducing queue.
- Optimize `subhg` function to improve performance by using a set for decided vertices and reducing iterations.

- Replace `region_cache.jl` with direct region management in `problems.jl`.
- Update variable and tensor ID handling to use `Int` instead of custom structs.
- Enhance debug logging in various functions for better traceability.
- Refactor function signatures and internal logic for consistency and clarity.

… efficiency and clarity.