Right
(fromList
 [((νx. x) + (μy. (νx. x) + y),fromList [
                (κ₁ 〈〉,κ₁ 〈〉),
                (κ₂ (α (κ₁ 〈〉)),κ₂ (α (κ₁ 〈〉)))
               ]
  ),
  (μy. (νx. x) + y,fromList [
          (α (κ₁ 〈〉),α (κ₁ 〈〉)),
          (α (κ₂ (α (κ₁ 〈〉))),α (κ₂ (α (κ₁ 〈〉))))
         ]
  ),
  ((μy. (νx. x) + y) × (νy. (μy. (νx. x) + y) × y),fromList [
                          (o1Out,o2Out),
                          (o1Out,o3Out)
                         ]
  ),
  (νx. x,fromList [
          (〈〉,〈〉)
         ]
  ),
  (νy. (μy. (νx. x) + y) × y,fromList [
          (o1,o2),
          (o1,o3)
         ]
  )
 ])

Just
(Left
 (fromList
  [(Sum oneT nat,
    fromList
    [(inj1 (f),inj1 (f)),
     (inj2 (in (inj1 (f))),inj2 (in (inj1 (f))))
    ]),
   (nat,
    fromList
    [(in (inj1 (f)),in (inj1 (f))),
     (in (inj2 (in (inj1 (f)))),in (inj2 (in (inj1 (f)))))
    ]),
   (Prod nat (stream nat),
    fromList [(o1Out,o1Out)]),
   (Gfp "x" (PT "x"),
    fromList [(f,f)]),
   (stream nat,
    fromList [(o1,o1)])
  ]
 )
)

Left
(fromList
 [(nat × (stream nat),
   fromList [ξ funky,ξ (π₂ f)]),
  stream nat,
   fromList [π₂ f,π₂ (ξ (π₂ f))])
 ]
)

Left
(fromList
 [(nat × stream nat,
   fromList [ξ (π₂ f)]),
  (stream nat,
   fromList [π₂ f,π₂ (ξ (π₂ f))])])
