WORST_CASE(?,O(n^2))

Solution:
---------

  :: :: [A(0, 0) x A(15, 0)] -(15)-> A(15, 0)
  :: :: [A(0, 0) x A(1, 0)] -(1)-> A(1, 0)
  :: :: [A(0, 0) x A(0, 0)] -(0)-> A(0, 1)
  append :: [A(15, 0) x A(3, 0)] -(2)-> A(1, 0)
  append#1 :: [A(15, 0) x A(3, 0)] -(1)-> A(1, 0)
  leaf :: [] -(0)-> A(0, 15)
  nil :: [] -(0)-> A(15, 0)
  nil :: [] -(0)-> A(7, 7)
  node :: [A(15, 15) x A(15, 15) x A(15, 15)] -(15)-> A(0, 15)
  node :: [A(0, 0) x A(0, 0) x A(0, 0)] -(0)-> A(0, 0)
  subtrees :: [A(7, 15)] -(4)-> A(7, 1)
  subtrees#1 :: [A(0, 15)] -(3)-> A(0, 1)
  subtrees#2 :: [A(15, 1) x A(0, 0) x A(7, 15) x A(7, 0)] -(8)-> A(0, 1)
  subtrees#3 :: [A(4, 3) x A(15, 1) x A(0, 0) x A(0, 0) x A(1, 0)] -(3)-> A(0, 1)


Cost Free Signatures:
---------------------

  :: :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0)
  :: :: [A_cf(0, 0) x A_cf(7, 0)] -(7)-> A_cf(7, 2)
  :: :: [A_cf(0, 0) x A_cf(7, 0)] -(7)-> A_cf(7, 0)
  :: :: [A_cf(0, 0) x A_cf(7, 0)] -(7)-> A_cf(7, 8)
  :: :: [A_cf(0, 0) x A_cf(8, 0)] -(8)-> A_cf(8, 8)
  :: :: [A_cf(0, 0) x A_cf(8, 0)] -(8)-> A_cf(8, 0)
  :: :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 10)
  :: :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 8)
  append :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0)
  append :: [A_cf(7, 0) x A_cf(7, 0)] -(0)-> A_cf(7, 0)
  append :: [A_cf(8, 0) x A_cf(8, 0)] -(0)-> A_cf(8, 0)
  append :: [A_cf(0, 0) x A_cf(0, 8)] -(0)-> A_cf(0, 8)
  append#1 :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0)
  append#1 :: [A_cf(7, 0) x A_cf(7, 0)] -(0)-> A_cf(7, 0)
  append#1 :: [A_cf(8, 0) x A_cf(8, 0)] -(0)-> A_cf(8, 0)
  append#1 :: [A_cf(0, 0) x A_cf(0, 8)] -(0)-> A_cf(0, 8)
  leaf :: [] -(0)-> A_cf(7, 0)
  leaf :: [] -(0)-> A_cf(8, 0)
  leaf :: [] -(0)-> A_cf(0, 0)
  nil :: [] -(0)-> A_cf(0, 0)
  nil :: [] -(0)-> A_cf(11, 2)
  nil :: [] -(0)-> A_cf(7, 0)
  nil :: [] -(0)-> A_cf(2, 2)
  nil :: [] -(0)-> A_cf(10, 2)
  nil :: [] -(0)-> A_cf(8, 0)
  nil :: [] -(0)-> A_cf(2, 10)
  node :: [A_cf(7, 0) x A_cf(7, 0) x A_cf(7, 0)] -(7)-> A_cf(7, 0)
  node :: [A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0)
  node :: [A_cf(8, 0) x A_cf(8, 0) x A_cf(8, 0)] -(8)-> A_cf(8, 0)
  subtrees :: [A_cf(7, 0)] -(0)-> A_cf(7, 0)
  subtrees :: [A_cf(8, 0)] -(0)-> A_cf(0, 0)
  subtrees :: [A_cf(8, 0)] -(0)-> A_cf(8, 0)
  subtrees :: [A_cf(0, 0)] -(0)-> A_cf(0, 8)
  subtrees#1 :: [A_cf(7, 0)] -(0)-> A_cf(7, 0)
  subtrees#1 :: [A_cf(8, 0)] -(0)-> A_cf(0, 0)
  subtrees#1 :: [A_cf(8, 0)] -(0)-> A_cf(8, 0)
  subtrees#1 :: [A_cf(0, 0)] -(0)-> A_cf(0, 8)
  subtrees#2 :: [A_cf(7, 0) x A_cf(0, 0) x A_cf(7, 0) x A_cf(2, 0)] -(7)-> A_cf(7, 0)
  subtrees#2 :: [A_cf(0, 0) x A_cf(0, 0) x A_cf(8, 0) x A_cf(0, 0)] -(4)-> A_cf(0, 0)
  subtrees#2 :: [A_cf(8, 0) x A_cf(0, 0) x A_cf(8, 0) x A_cf(0, 0)] -(8)-> A_cf(8, 0)
  subtrees#2 :: [A_cf(0, 8) x A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 8)
  subtrees#3 :: [A_cf(7, 0) x A_cf(7, 0) x A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(7)-> A_cf(7, 0)
  subtrees#3 :: [A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(4)-> A_cf(0, 0)
  subtrees#3 :: [A_cf(8, 0) x A_cf(8, 0) x A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(8)-> A_cf(8, 0)
  subtrees#3 :: [A_cf(0, 8) x A_cf(0, 2) x A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 8)


Base Constructors:
------------------
  ::_A :: [A(0) x A(0)] -(0)-> A(0)
  leaf_A :: [] -(0)-> A(1, 0)
  leaf_A :: [] -(0)-> A(0, 1)
  nil_A :: [] -(0)-> A(1, 0)
  nil_A :: [] -(0)-> A(0, 1)
  node_A :: [A(1, 0) x A(1, 0) x A(1, 0)] -(1)-> A(1, 0)
  node_A :: [A(1, 1) x A(1, 1) x A(1, 1)] -(1)-> A(0, 1)