The tth step simple amalgamation problem in Equation (2) can be expressed as min(𝑗,𝑗′)∈𝒫𝑡−1{∑𝑖<𝑖′[min(𝑥𝑖𝑗,𝑡−1,𝑥𝑖′𝑗,𝑡−1)+min(𝑥𝑖𝑗′,𝑡−1,𝑥𝑖′𝑗′,𝑡−1)−min(𝑥𝑖𝑗,𝑡−1+𝑥𝑖𝑗′,𝑡−...