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I am working on a small prolog application to solve the Skyscrapers and Fences puzzle. An unsolved puzzle: A solved puzzle: When I pass the program already solved puzzles it is quick, almost instantaneous, to validate it for me. When I pass the program really small puzzles (2x2, for example, with modified rules, of course), it is also quite fast to find a solution. The problem is on computing puzzles with the "native" size of 6x6. I've left it running for 5 or so hours before aborting it. Way too much time. I've found that the part that takes the longest is the "fences" one, not the "skyscrapers". Running "skyscrapers" separately results in a fast solution. Here's my algorithm for fences: Vertices are represented by numbers, 0 means the path doesn't pass through that particular vertex, > 1 represents that vertex's order in the path. Constrain each cell to have the appropriate amount of lines surrounding it. That means that two vertexes are connected if they have sequential numbers, e.g., 1 -> 2, 2 -> 1, 1 -> Max , Max -> 1 ( Max is the number for the last vertex in the path. computed via maximum/2 ) Make sure each non-zero vertex has at least two neighboring vertices with sequential numbers Constrain Max to be equal to (BoardWidth + 1)^2 - NumberOfZeros ( BoardWidth+1 is the number of vertices along the edge and NumberOfZeros is computed via count/4 ). Use nvalue(Vertices, Max + 1) to make sure the number of distinct values in Verti

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