Legacy systems are business-critical software systems whose failure can have a significant impact on the business. Yet, their maintenance and adaption to changed requirements consume a considerable amount of the total software development costs. Frequently, domain experts and developers involved in the original development are not available anymore, making it difficult to adapt a legacy system without introducing bugs or unwanted behavior. This results in a dilemma: businesses are reluctant to change a working system, while at the same time struggling with its high maintenance costs. We propose the concept of Structured Software Reengineering replacing the ad hoc forward engineering part of a reengineering process with the application of behavior-preserving, proven-correct transformations improving nonfunctional program properties. Such transformations preserve valuable business logic while improving properties such as maintainability, performance, or portability to new platforms. Manually encoding and proving such transformations for industrial programming languages, for example, in interactive proof assistants, is a major challenge requiring deep expert knowledge. Existing frameworks for automatically proving transformation rules have limited expressiveness and are restricted to particular target applications such as compilation or peep-hole optimizations. We present Abstract Execution, a specification and verification framework for statement-based program transformation rules on JAVA programs building on symbolic execution. Abstract Execution supports universal quantification over statements or expressions and addresses properties about the (big-step) behavior of programs. Since this class of properties is useful for a plethora of applications, Abstract Execution bridges the gap between expressiveness and automation. In many cases, fully automatic proofs are in possible. We explain REFINITY, a workbench for modeling and proving statement-level JAVA transformation rules, and discuss our applications of Abstract Execution to code refactoring, cost analysis of program transformations, and transformations reshaping programs for the application of parallel design patterns.