In this research work, we perform text line segmentation directly in compressed representation of an unconstrained handwritten document image. In this relation, we make use of text line terminal points which is the current state-of-the-art. The terminal points spotted along both margins (left and right) of a document image for every text line are considered as source and target respectively. The tunneling algorithm uses a single agent (or robot) to identify the coordinate positions in the compressed representation to perform text-line segmentation of the document. The agent starts at a source point and progressively tunnels a path routing in between two adjacent text lines and reaches the probable target. The agent's navigation path from source to the target bypassing obstacles, if any, results in segregating the two adjacent text lines. However, the target point would be known only when the agent reaches the destination; this is applicable for all source points and henceforth we could analyze the correspondence between source and target nodes. Artificial Intelligence in Expert systems, dynamic programming and greedy strategies are employed for every search space while tunneling. An exhaustive experimentation is carried out on various benchmark datasets including ICDAR13 and the performances are reported.