WORST_CASE(?,O(n^3))
* Step 1: Ara WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
            choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
            choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
            insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
            insert(x,nil()) -> cons(x,nil())
            sort(cons(x,y)) -> insert(x,sort(y))
            sort(nil()) -> nil()
        - Signature:
            {choose/4,insert/2,sort/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {choose,insert,sort} and constructors {0,cons,nil,s}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> A(1, 0, 0)
          0 :: [] -(0)-> A(0, 0, 0)
          choose :: [A(2, 0, 0) x A(0, 2, 0) x A(0, 0, 0) x A(1, 0, 0)] -(0)-> A(0, 0, 0)
          cons :: [A(0, 0, 0) x A(2, 2, 0)] -(2)-> A(0, 2, 0)
          cons :: [A(2, 0, 0) x A(2, 2, 0)] -(2)-> A(2, 2, 0)
          cons :: [A(2, 0, 0) x A(2, 2, 2)] -(2)-> A(0, 0, 2)
          cons :: [A(0, 0, 0) x A(0, 0, 0)] -(0)-> A(0, 0, 0)
          cons :: [A(2, 0, 0) x A(0, 0, 0)] -(0)-> A(2, 0, 0)
          insert :: [A(2, 0, 0) x A(2, 2, 0)] -(1)-> A(0, 0, 0)
          nil :: [] -(0)-> A(2, 2, 0)
          nil :: [] -(0)-> A(0, 0, 2)
          nil :: [] -(0)-> A(2, 0, 3)
          nil :: [] -(0)-> A(1, 2, 2)
          s :: [A(1, 0, 0)] -(1)-> A(1, 0, 0)
          s :: [A(0, 0, 0)] -(0)-> A(0, 0, 0)
          sort :: [A(0, 0, 2)] -(1)-> A(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
          0 :: [] -(0)-> A_cf(0, 0, 0)
          choose :: [A_cf(0, 0, 0) x A_cf(0, 0, 0) x A_cf(0, 0, 0) x A_cf(0, 0, 0)] -(0)-> A_cf(0, 0, 0)
          choose :: [A_cf(2, 0, 0) x A_cf(2, 2, 0) x A_cf(0, 0, 0) x A_cf(0, 0, 0)] -(2)-> A_cf(2, 2, 0)
          cons :: [A_cf(0, 0, 0) x A_cf(0, 0, 0)] -(0)-> A_cf(0, 0, 0)
          cons :: [A_cf(2, 0, 0) x A_cf(2, 2, 0)] -(2)-> A_cf(2, 2, 0)
          insert :: [A_cf(0, 0, 0) x A_cf(0, 0, 0)] -(0)-> A_cf(0, 0, 0)
          insert :: [A_cf(2, 0, 0) x A_cf(2, 2, 0)] -(2)-> A_cf(2, 2, 0)
          nil :: [] -(0)-> A_cf(0, 0, 0)
          nil :: [] -(0)-> A_cf(2, 2, 0)
          nil :: [] -(0)-> A_cf(3, 2, 1)
          s :: [A_cf(0, 0, 0)] -(0)-> A_cf(0, 0, 0)
          sort :: [A_cf(2, 2, 0)] -(0)-> A_cf(2, 2, 0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1, 0, 0)
          0_A :: [] -(0)-> A(0, 1, 0)
          0_A :: [] -(1)-> A(0, 0, 1)
          cons_A :: [A(1, 0, 0) x A(0, 0, 0)] -(0)-> A(1, 0, 0)
          cons_A :: [A(0, 0, 0) x A(1, 1, 0)] -(1)-> A(0, 1, 0)
          cons_A :: [A(1, 0, 0) x A(1, 1, 1)] -(1)-> 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, 0, 0)] -(0)-> A(0, 1, 0)
          s_A :: [A(0, 0, 0)] -(1)-> A(0, 0, 1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
        choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
        choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
        insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
        insert(x,nil()) -> cons(x,nil())
        sort(cons(x,y)) -> insert(x,sort(y))
        sort(nil()) -> nil()
    - Signature:
        {choose/4,insert/2,sort/1} / {0/0,cons/2,nil/0,s/1}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {choose,insert,sort} and constructors {0,cons,nil,s}
Following problems could not be solved:
  - Strict TRS:
      choose(x,cons(v,w),y,0()) -> cons(x,cons(v,w))
      choose(x,cons(v,w),0(),s(z)) -> cons(v,insert(x,w))
      choose(x,cons(v,w),s(y),s(z)) -> choose(x,cons(v,w),y,z)
      insert(x,cons(v,w)) -> choose(x,cons(v,w),x,v)
      insert(x,nil()) -> cons(x,nil())
      sort(cons(x,y)) -> insert(x,sort(y))
      sort(nil()) -> nil()
  - Signature:
      {choose/4,insert/2,sort/1} / {0/0,cons/2,nil/0,s/1}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {choose,insert,sort} and constructors {0,cons,nil,s}
WORST_CASE(?,O(n^3))