ABC + DEF = GHI
GDA + HEB = IFC
There are two sets of simultaneous solutions for the above 2 alphametics,
one being a 90o rotation of the other.
No leading zeroes.
(In reply to program and solution (spoilers)
Your solution as well as the remark that it is not a "rotation" relation are correct.
Both sets of solutions are zeroless and the division of the 9 digits (= 3 triplets) in both is fitting your description.
b=8, i =9, d=1 in both while (c,h )=(2,3) in one and (3,2) in other, and (a,e) ,(f,g) correspond in similar way to (4,5), (7,6) accordingly.
So "one man's column is another man's row, ignoring order,"
Tnx for your correction.