WORST_CASE(?,O(n^3))
* Step 1: Ara WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            first(0(),X) -> nil()
            first(s(X),cons(Y)) -> cons(Y)
            half(0()) -> 0()
            half(dbl(X)) -> X
            half(s(0())) -> 0()
            half(s(s(X))) -> s(half(X))
            sqr(0()) -> 0()
            sqr(s(X)) -> s(add(sqr(X),dbl(X)))
            terms(N) -> cons(recip(sqr(N)))
        - Signature:
            {add/2,dbl/1,first/2,half/1,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {add,dbl,first,half,sqr,terms} and constructors {0,cons
            ,nil,recip,s}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> A(1, 0, 0)
          0 :: [] -(0)-> A(0, 3, 0)
          0 :: [] -(0)-> A(4, 2, 8)
          0 :: [] -(0)-> A(10, 0, 12)
          0 :: [] -(0)-> A(4, 1, 7)
          0 :: [] -(0)-> A(1, 1, 7)
          add :: [A(1, 0, 0) x A(0, 0, 0)] -(8)-> A(0, 0, 0)
          cons :: [A(1, 0, 0)] -(13)-> A(5, 1, 13)
          cons :: [A(1, 0, 0)] -(8)-> A(1, 1, 8)
          cons :: [A(2, 0, 0)] -(4)-> A(9, 2, 4)
          dbl :: [A(0, 3, 0)] -(1)-> A(1, 0, 0)
          first :: [A(4, 2, 8) x A(5, 1, 13)] -(5)-> A(1, 1, 4)
          half :: [A(1, 0, 0)] -(8)-> A(0, 0, 0)
          nil :: [] -(0)-> A(4, 4, 10)
          recip :: [A(0, 0, 0)] -(0)-> A(12, 3, 6)
          s :: [A(1, 0, 0)] -(1)-> A(1, 0, 0)
          s :: [A(3, 3, 0)] -(3)-> A(0, 3, 0)
          s :: [A(6, 10, 8)] -(6)-> A(4, 2, 8)
          s :: [A(10, 12, 12)] -(10)-> A(10, 0, 12)
          s :: [A(0, 0, 0)] -(0)-> A(0, 0, 0)
          sqr :: [A(10, 0, 12)] -(5)-> A(0, 0, 0)
          terms :: [A(12, 14, 14)] -(14)-> A(2, 0, 2)
        
        
        Cost-free Signatures used:
        --------------------------
          0 :: [] -(0)-> A_cf(0, 0, 0)
          0 :: [] -(0)-> A_cf(0, 0, 3)
          0 :: [] -(0)-> A_cf(1, 5, 9)
          0 :: [] -(0)-> A_cf(0, 0, 2)
          0 :: [] -(0)-> A_cf(0, 8, 0)
          0 :: [] -(0)-> A_cf(4, 0, 2)
          0 :: [] -(0)-> A_cf(1, 0, 0)
          0 :: [] -(0)-> A_cf(2, 0, 0)
          0 :: [] -(0)-> A_cf(9, 0, 2)
          add :: [A_cf(0, 0, 0) x A_cf(0, 0, 0)] -(0)-> A_cf(0, 0, 0)
          add :: [A_cf(1, 0, 0) x A_cf(1, 0, 0)] -(0)-> A_cf(1, 0, 0)
          dbl :: [A_cf(1, 5, 9)] -(2)-> A_cf(0, 0, 0)
          dbl :: [A_cf(1, 5, 9)] -(0)-> A_cf(0, 0, 0)
          dbl :: [A_cf(2, 0, 0)] -(1)-> A_cf(1, 0, 0)
          half :: [A_cf(0, 0, 0)] -(1)-> A_cf(0, 0, 0)
          s :: [A_cf(0, 0, 0)] -(0)-> A_cf(0, 0, 0)
          s :: [A_cf(6, 14, 9)] -(6)-> A_cf(1, 5, 9)
          s :: [A_cf(8, 8, 0)] -(8)-> A_cf(0, 8, 0)
          s :: [A_cf(1, 0, 0)] -(1)-> A_cf(1, 0, 0)
          s :: [A_cf(2, 0, 0)] -(2)-> A_cf(2, 0, 0)
          sqr :: [A_cf(0, 8, 0)] -(0)-> A_cf(1, 0, 0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1, 0, 0)
          0_A :: [] -(0)-> A(0, 1, 0)
          0_A :: [] -(0)-> A(0, 0, 1)
          cons_A :: [A(0, 0, 0)] -(0)-> A(1, 0, 0)
          cons_A :: [A(1, 0, 0)] -(0)-> A(0, 1, 0)
          cons_A :: [A(0, 0, 0)] -(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)
          recip_A :: [A(0, 0, 0)] -(0)-> A(1, 0, 0)
          recip_A :: [A(0, 0, 0)] -(0)-> A(0, 1, 0)
          recip_A :: [A(0, 0, 0)] -(0)-> A(0, 0, 1)
          s_A :: [A(1, 0, 0)] -(1)-> A(1, 0, 0)
          s_A :: [A(1, 1, 0)] -(1)-> A(0, 1, 0)
          s_A :: [A(0, 1, 1)] -(0)-> A(0, 0, 1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        add(0(),X) -> X
        add(s(X),Y) -> s(add(X,Y))
        dbl(0()) -> 0()
        dbl(s(X)) -> s(s(dbl(X)))
        first(0(),X) -> nil()
        first(s(X),cons(Y)) -> cons(Y)
        half(0()) -> 0()
        half(dbl(X)) -> X
        half(s(0())) -> 0()
        half(s(s(X))) -> s(half(X))
        sqr(0()) -> 0()
        sqr(s(X)) -> s(add(sqr(X),dbl(X)))
        terms(N) -> cons(recip(sqr(N)))
    - Signature:
        {add/2,dbl/1,first/2,half/1,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/1}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {add,dbl,first,half,sqr,terms} and constructors {0,cons
        ,nil,recip,s}
Following problems could not be solved:
  - Strict TRS:
      add(0(),X) -> X
      add(s(X),Y) -> s(add(X,Y))
      dbl(0()) -> 0()
      dbl(s(X)) -> s(s(dbl(X)))
      first(0(),X) -> nil()
      first(s(X),cons(Y)) -> cons(Y)
      half(0()) -> 0()
      half(dbl(X)) -> X
      half(s(0())) -> 0()
      half(s(s(X))) -> s(half(X))
      sqr(0()) -> 0()
      sqr(s(X)) -> s(add(sqr(X),dbl(X)))
      terms(N) -> cons(recip(sqr(N)))
  - Signature:
      {add/2,dbl/1,first/2,half/1,sqr/1,terms/1} / {0/0,cons/1,nil/0,recip/1,s/1}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {add,dbl,first,half,sqr,terms} and constructors {0,cons
      ,nil,recip,s}
WORST_CASE(?,O(n^3))