WORST_CASE(?,O(n^3))

Solution:
---------

  "0" :: [] -(0)-> "A"(0, 0, 0)
  "0" :: [] -(0)-> "A"(1, 0, 0)
  "add" :: ["A"(9, 0, 0) x "A"(12, 3, 3)] -(9)-> "A"(9, 3, 3)
  "add" :: ["A"(8, 0, 0) x "A"(12, 3, 3)] -(8)-> "A"(8, 4, 3)
  "add" :: ["A"(6, 0, 0) x "A"(9, 3, 3)] -(6)-> "A"(6, 3, 3)
  "add" :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
  "eq" :: ["A"(0, 0, 0) x "A"(1, 0, 0)] -(1)-> "A"(15, 15, 15)
  "false" :: [] -(0)-> "A"(0, 0, 8)
  "false" :: [] -(0)-> "A"(15, 15, 15)
  "ifrm" :: ["A"(0, 0, 8) x "A"(0, 0, 0) x "A"(8, 4, 3)] -(2)-> "A"(6, 3, 3)
  "nil" :: [] -(0)-> "A"(9, 3, 3)
  "nil" :: [] -(0)-> "A"(6, 3, 3)
  "nil" :: [] -(0)-> "A"(15, 15, 15)
  "nil" :: [] -(0)-> "A"(12, 0, 12)
  "purge" :: ["A"(6, 3, 3)] -(6)-> "A"(0, 0, 0)
  "rm" :: ["A"(0, 0, 0) x "A"(9, 3, 3)] -(3)-> "A"(6, 3, 3)
  "s" :: ["A"(1, 0, 0)] -(1)-> "A"(1, 0, 0)
  "s" :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
  "true" :: [] -(0)-> "A"(0, 0, 8)
  "true" :: [] -(0)-> "A"(15, 15, 15)


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

  "0" :: [] -(0)-> "A"_cf(0, 0, 0)
  "add" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "add" :: ["A"_cf(3, 0, 0) x "A"_cf(3, 0, 0)] -(3)-> "A"_cf(3, 0, 0)
  "eq" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "eq" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(15, 15, 6)
  "eq" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(12, 12, 12)
  "false" :: [] -(0)-> "A"_cf(0, 0, 0)
  "false" :: [] -(0)-> "A"_cf(11, 15, 6)
  "false" :: [] -(0)-> "A"_cf(15, 15, 6)
  "false" :: [] -(0)-> "A"_cf(15, 15, 7)
  "false" :: [] -(0)-> "A"_cf(12, 12, 15)
  "false" :: [] -(0)-> "A"_cf(12, 12, 14)
  "ifrm" :: ["A"_cf(11, 15, 6) x "A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "ifrm" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0) x "A"_cf(3, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "ifrm" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0) x "A"_cf(3, 0, 0)] -(0)-> "A"_cf(3, 0, 0)
  "ifrm" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "nil" :: [] -(0)-> "A"_cf(0, 0, 0)
  "nil" :: [] -(0)-> "A"_cf(12, 14, 15)
  "nil" :: [] -(0)-> "A"_cf(4, 4, 14)
  "nil" :: [] -(0)-> "A"_cf(3, 0, 0)
  "nil" :: [] -(0)-> "A"_cf(6, 14, 14)
  "nil" :: [] -(0)-> "A"_cf(15, 15, 0)
  "purge" :: ["A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "rm" :: ["A"_cf(0, 0, 0) x "A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "rm" :: ["A"_cf(0, 0, 0) x "A"_cf(3, 0, 0)] -(1)-> "A"_cf(0, 0, 0)
  "rm" :: ["A"_cf(0, 0, 0) x "A"_cf(3, 0, 0)] -(0)-> "A"_cf(3, 0, 0)
  "s" :: ["A"_cf(0, 0, 0)] -(0)-> "A"_cf(0, 0, 0)
  "true" :: [] -(0)-> "A"_cf(0, 0, 0)
  "true" :: [] -(0)-> "A"_cf(11, 15, 6)
  "true" :: [] -(0)-> "A"_cf(15, 15, 7)
  "true" :: [] -(0)-> "A"_cf(15, 15, 6)
  "true" :: [] -(0)-> "A"_cf(12, 12, 12)


Base Constructors:
------------------
  "\"0\"_A" :: [] -(0)-> "A"(1, 0, 0)
  "\"0\"_A" :: [] -(0)-> "A"(0, 1, 0)
  "\"0\"_A" :: [] -(1)-> "A"(0, 0, 1)
  "\"add\"_A" :: ["A"(1, 0, 0) x "A"(1, 0, 0)] -(1)-> "A"(1, 0, 0)
  "\"add\"_A" :: ["A"(0, 0, 0) x "A"(1, 0, 0)] -(0)-> "A"(0, 1, 0)
  "\"add\"_A" :: ["A"(0, 0, 0) x "A"(0, 1, 1)] -(0)-> "A"(0, 0, 1)
  "\"false\"_A" :: [] -(0)-> "A"(1, 0, 0)
  "\"false\"_A" :: [] -(0)-> "A"(0, 1, 0)
  "\"false\"_A" :: [] -(0)-> "A"(0, 0, 1)
  "\"nil\"_A" :: [] -(0)-> "A"(1, 0, 0)
  "\"nil\"_A" :: [] -(0)-> "A"(0, 1, 0)
  "\"nil\"_A" :: [] -(0)-> "A"(0, 0, 1)
  "\"s\"_A" :: ["A"(1, 0, 0)] -(1)-> "A"(1, 0, 0)
  "\"s\"_A" :: ["A"(0, 1, 0)] -(1)-> "A"(0, 1, 0)
  "\"s\"_A" :: ["A"(1, 0, 0)] -(0)-> "A"(0, 0, 1)
  "\"true\"_A" :: [] -(0)-> "A"(1, 0, 0)
  "\"true\"_A" :: [] -(0)-> "A"(0, 1, 0)
  "\"true\"_A" :: [] -(0)-> "A"(0, 0, 1)