We developed a parallel solver for which the number of processors in use depends on the intrinsic complexity of the input system, that is on geometry of its solution set. We extended the sequential Triade algorithm that uses increamental solving and organizes the computation into a task management diaphram in favour of parallel execution. Rich parallel opportunities are created and load balancing are achieved by combining modular methods and solving by decreasing order of dimension. We realized an implementation on a SMP using multi-processed parallelism based on server programs created in Aldor and inter-process data communication through shared memory segments. Implementation challenges include sophisticated methematical objects encoding, irregular task scheduling, dynamic process management and heavy data communication.