WORST_CASE(?,O(n^2))
* Step 1: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            p(f(f(x))) -> q(f(g(x)))
            p(g(g(x))) -> q(g(f(x)))
            q(f(f(x))) -> p(f(g(x)))
            q(g(g(x))) -> p(g(f(x)))
        - Signature:
            {p/1,q/1} / {f/1,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p,q} and constructors {f,g}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3}
    + Details:
        Signatures used:
        ----------------
          f :: [A(2, 0)] -(2)-> A(2, 2)
          f :: [A(2, 0)] -(2)-> A(2, 0)
          f :: [A(1, 0)] -(1)-> A(1, 1)
          f :: [A(1, 0)] -(1)-> A(1, 0)
          f :: [A(1, 0)] -(1)-> A(1, 4)
          f :: [A(0, 0)] -(0)-> A(0, 8)
          f :: [A(2, 0)] -(2)-> A(2, 14)
          g :: [A(0, 2)] -(2)-> A(2, 2)
          g :: [A(0, 2)] -(2)-> A(0, 2)
          g :: [A(0, 1)] -(1)-> A(1, 1)
          g :: [A(0, 1)] -(1)-> A(0, 1)
          g :: [A(0, 0)] -(0)-> A(13, 0)
          g :: [A(0, 1)] -(1)-> A(7, 1)
          g :: [A(0, 0)] -(0)-> A(5, 0)
          g :: [A(0, 2)] -(2)-> A(8, 2)
          p :: [A(2, 2)] -(0)-> A(12, 12)
          q :: [A(1, 1)] -(1)-> A(12, 12)
        
        
        Cost-free Signatures used:
        --------------------------
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 2)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 0)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 6)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 10)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 14)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 1)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 8)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 15)
          f :: [A_cf(6, 0)] -(6)-> A_cf(6, 0)
          f :: [A_cf(7, 0)] -(7)-> A_cf(7, 6)
          f :: [A_cf(7, 0)] -(7)-> A_cf(7, 0)
          f :: [A_cf(6, 0)] -(6)-> A_cf(6, 10)
          f :: [A_cf(7, 0)] -(7)-> A_cf(7, 7)
          f :: [A_cf(5, 0)] -(5)-> A_cf(5, 0)
          f :: [A_cf(7, 0)] -(7)-> A_cf(7, 15)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 5)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 3)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 9)
          f :: [A_cf(6, 0)] -(6)-> A_cf(6, 8)
          f :: [A_cf(4, 0)] -(4)-> A_cf(4, 0)
          f :: [A_cf(7, 0)] -(7)-> A_cf(7, 9)
          f :: [A_cf(0, 0)] -(0)-> A_cf(0, 4)
          g :: [A_cf(0, 2)] -(2)-> A_cf(0, 2)
          g :: [A_cf(0, 6)] -(6)-> A_cf(0, 6)
          g :: [A_cf(0, 0)] -(0)-> A_cf(14, 0)
          g :: [A_cf(0, 5)] -(5)-> A_cf(13, 5)
          g :: [A_cf(0, 1)] -(1)-> A_cf(0, 1)
          g :: [A_cf(0, 0)] -(0)-> A_cf(10, 0)
          g :: [A_cf(0, 2)] -(2)-> A_cf(9, 2)
          g :: [A_cf(0, 1)] -(1)-> A_cf(1, 1)
          g :: [A_cf(0, 0)] -(0)-> A_cf(6, 0)
          g :: [A_cf(0, 0)] -(0)-> A_cf(0, 0)
          g :: [A_cf(0, 6)] -(6)-> A_cf(7, 6)
          g :: [A_cf(0, 0)] -(0)-> A_cf(15, 0)
          g :: [A_cf(0, 0)] -(0)-> A_cf(5, 0)
          g :: [A_cf(0, 0)] -(0)-> A_cf(8, 0)
          g :: [A_cf(0, 5)] -(5)-> A_cf(0, 5)
          g :: [A_cf(0, 5)] -(5)-> A_cf(8, 5)
          g :: [A_cf(0, 0)] -(0)-> A_cf(9, 0)
          g :: [A_cf(0, 3)] -(3)-> A_cf(0, 3)
          g :: [A_cf(0, 8)] -(8)-> A_cf(1, 8)
          g :: [A_cf(0, 0)] -(0)-> A_cf(4, 0)
          p :: [A_cf(0, 6)] -(0)-> A_cf(0, 0)
          p :: [A_cf(0, 1)] -(0)-> A_cf(0, 0)
          p :: [A_cf(7, 6)] -(0)-> A_cf(0, 0)
          p :: [A_cf(5, 0)] -(0)-> A_cf(0, 0)
          p :: [A_cf(0, 5)] -(0)-> A_cf(0, 0)
          p :: [A_cf(6, 0)] -(0)-> A_cf(0, 0)
          q :: [A_cf(0, 2)] -(0)-> A_cf(0, 0)
          q :: [A_cf(6, 0)] -(0)-> A_cf(0, 0)
          q :: [A_cf(0, 5)] -(0)-> A_cf(0, 0)
          q :: [A_cf(0, 3)] -(0)-> A_cf(0, 0)
          q :: [A_cf(0, 0)] -(10)-> A_cf(0, 0)
          q :: [A_cf(4, 0)] -(0)-> A_cf(0, 0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          f_A :: [A(1, 0)] -(1)-> A(1, 0)
          f_A :: [A(0, 0)] -(0)-> A(0, 1)
          g_A :: [A(0, 0)] -(0)-> A(1, 0)
          g_A :: [A(0, 1)] -(1)-> A(0, 1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        p(f(f(x))) -> q(f(g(x)))
        p(g(g(x))) -> q(g(f(x)))
        q(f(f(x))) -> p(f(g(x)))
        q(g(g(x))) -> p(g(f(x)))
    - Signature:
        {p/1,q/1} / {f/1,g/1}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {p,q} and constructors {f,g}
Following problems could not be solved:
  - Strict TRS:
      p(f(f(x))) -> q(f(g(x)))
      p(g(g(x))) -> q(g(f(x)))
      q(f(f(x))) -> p(f(g(x)))
      q(g(g(x))) -> p(g(f(x)))
  - Signature:
      {p/1,q/1} / {f/1,g/1}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {p,q} and constructors {f,g}
WORST_CASE(?,O(n^2))