Research solving / simplifying system of co-recursive symbolic equations

[KinanBab]

Attempt to find a reasonable closed form that is "nice looking"

Cases to consider:

1. No recursion: reduces to inline and simplify
2. Single function recursion: inline, simplify, solve recurrence
3. Co-recursive functions: ?

Solving recurrences:

1. Masters or Akra/Bazzi theorem: asymptotic
2. Outsource to wolfram or other algerbra systems
3. Pattern / rule based
4. Heurstic driven search?

Prove that closed form is correct solution, important for 3 and 4 (maybe 2?):

1. Induction (in style of sums)
2. SMT?