Scavenging the idling computation resources at the enormous number of mobile devices can provide a powerful platform for local mobile cloud computing. The vision can be realized by peer-to-peer cooperative computing between edge devices, referred to as co-computing. This paper considers a co-computing system where a user offloads computation of input-data to a helper. The helper controls the offloading process for the objective of minimizing the user's energy consumption based on a predicted helper's CPU-idling profile that specifies the amount of available computation resource for co-computing. Consider the scenario that the user has one-shot input-data arrival and the helper buffers offloaded bits. The problem for energy-efficient co-computing is formulated as two sub-problems: the slave problem corresponding to adaptive offloading and the master one to data partitioning. Given a fixed offloaded data size, the adaptive offloading aims at minimizing the energy consumption for offloading by controlling the offloading rate under the deadline and buffer constraints. By deriving the necessary and sufficient conditions for the optimal solution, we characterize the structure of the optimal policies and propose algorithms for computing the policies. Furthermore, we show that the problem of optimal data partitioning for offloading and local computing at the user is convex, admitting a simple solution using the sub-gradient method. Last, the developed design approach for co-computing is extended to the scenario of bursty data arrivals at the user accounting for data causality constraints. Simulation results verify the effectiveness of the proposed algorithms.