renameTree (Leaf 3.14) == Leaf 1
renameTree (Node "abc" (Node "xyz" (Leaf "abc") (Leaf ("ab"++"c"))) (Leaf "uv")) == (Node 1 (Node 2 (Leaf 1) (Leaf 1)) (Leaf 3)) {-corr.-}

mRT (Leaf 3.14) == Leaf 1
mRT (Node "abc" (Node "xyz" (Leaf "abc") (Leaf ("ab"++"c"))) (Leaf "uv")) == (Node 1 (Node 2 (Leaf 1) (Leaf 1)) (Leaf 3)) {-corr.-}

numberTree (Leaf3 3.14) == Leaf3 1
numberTree (Node3 "abc" (Node3 "xyz" (Leaf3 "abc") (Leaf3 "abc") (Leaf3 ("ab"++"c"))) (Leaf3 "abc") (Leaf3 "uv")) == (Node3 7 (Node3 4 (Leaf3 1) (Leaf3 2) (Leaf3 3)) (Leaf3 5) (Leaf3 6))

numberTreeMF (Leaf3 3.14) == Leaf3 1
numberTreeMF (Node3 "abc" (Node3 "xyz" (Leaf3 "abc") (Leaf3 "abc") (Leaf3 ("ab"++"c"))) (Leaf3 "abc") (Leaf3 "uv")) == (Node3 7 (Node3 4 (Leaf3 1) (Leaf3 2) (Leaf3 3)) (Leaf3 5) (Leaf3 6))