require 'set'
f = -> a {
  g = -> a {a.combination(2) {|x, y| break g.(a.tap {x.merge y; a.delete y}) if x.intersect? y}}
  h = a.map {|s| s.split('=')}.flatten.uniq.map.with_index.to_h
  a = a.map {|s| s.split('=').map {|k| h[k]}.to_set SortedSet}
  g.(a).map {|set| set.map &h.invert.method(:[])}
}
a = ["a1=a2", "b1=b2", "b3=b2", "c1=c2", "e1=e2",
"a3=a4", "c3=c4", "e1=e3", "a2=a4", "c3=c1",
"b3=a4", "c2=d1", "a4=a5", "d2=c1", "b4=b3", "d3=c3"]
p f.(a)
 

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