A data processing system is disclosed that includes an in-line accelerator and a processor. The system can be extended to include an in-line accelerator and system of multi-level accelerators and a processor. The in-line accelerator receives the incoming data elements and begins processing. Upon premature termination of the execution, the in-line accelerator transfers the execution to a processor (or the next level accelerator in a multi-level acceleration system). Transfer of execution includes transferring of data and control. The processor (or the next accelerator) either continues the execution of the in-line accelerator from the bailout point or restarts the execution. The necessary data must be transferred to the processor (or the next accelerator) to complete the execution.