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+title = "Rebuilding the correct order of arguments"
+author = "Yann Herklotz"
+tags = []
+categories = []
+backlinks = ["3a8g4"]
+forwardlinks = ["3a8g4b"]
+zettelid = "3a8g4a"
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+
+This has been corrected in another note ([\#3a8g4b]).
+
+We therefore have to recreate the correct order of the arguments based
+on the predecessors. The correctness of this might be quite hard to
+show, however, the idea of the algorithm is the following:
+
+1.  Find all the points of definition of the variables inside the φ
+    function, and get all the predecessors. The main idea is that the
+    definition points of the variables must necessarily dominate the
+    predecessor that should be used to select that variable. However,
+    the difficulty is that it might not uniquely dominate the
+    predecessor of the variable.
+2.  Find all the points of definition that dominate the minimum number
+    of predecessors. If there are more than one, this means that there
+    must be duplicate versions of the variable inside the φ function.
+3.  Take all the points where the number of predecessors that are
+    dominated by the point of definition also coincides with the number
+    of uses of that variable inside of the φ function.
+4.  Take the list of predecessors and map through it, always looking up
+    the variables that were assigned to that predecessor in the previous
+    step, and replace the predecessor in the list.
+5.  The result should be a correctly ordered list for the phi function,
+    which will work with an arbitrary order in the GSA input.
+
+  [\#3a8g4b]: /zettel/3a8g4b