WORST_CASE(?,O(n^1))
* Step 1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__eq(X,Y) -> false()
            a__eq(X1,X2) -> eq(X1,X2)
            a__eq(0(),0()) -> true()
            a__eq(s(X),s(Y)) -> a__eq(X,Y)
            a__inf(X) -> cons(X,inf(s(X)))
            a__inf(X) -> inf(X)
            a__length(X) -> length(X)
            a__length(cons(X,L)) -> s(length(L))
            a__length(nil()) -> 0()
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),X) -> nil()
            a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(eq(X1,X2)) -> a__eq(X1,X2)
            mark(false()) -> false()
            mark(inf(X)) -> a__inf(mark(X))
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
            mark(true()) -> true()
        - Signature:
            {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
            ,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0
            ,cons,eq,false,inf,length,nil,s,take,true}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = Z3}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> A(1)
          0 :: [] -(0)-> A(5)
          0 :: [] -(0)-> A(0)
          0 :: [] -(0)-> A(15)
          0 :: [] -(0)-> A(7)
          a__eq :: [A(1) x A(5)] -(8)-> A(0)
          a__inf :: [A(0)] -(4)-> A(0)
          a__length :: [A(0)] -(9)-> A(0)
          a__take :: [A(0) x A(0)] -(6)-> A(0)
          cons :: [A(0) x A(0)] -(0)-> A(0)
          cons :: [A(0) x A(15)] -(15)-> A(15)
          eq :: [A(15) x A(15)] -(15)-> A(15)
          eq :: [A(0) x A(0)] -(0)-> A(0)
          false :: [] -(0)-> A(15)
          false :: [] -(0)-> A(7)
          inf :: [A(15)] -(15)-> A(15)
          inf :: [A(0)] -(0)-> A(0)
          length :: [A(15)] -(15)-> A(15)
          length :: [A(0)] -(0)-> A(0)
          mark :: [A(15)] -(8)-> A(0)
          nil :: [] -(0)-> A(0)
          nil :: [] -(0)-> A(15)
          nil :: [] -(0)-> A(7)
          s :: [A(1)] -(1)-> A(1)
          s :: [A(5)] -(5)-> A(5)
          s :: [A(0)] -(0)-> A(0)
          s :: [A(15)] -(15)-> A(15)
          take :: [A(15) x A(15)] -(15)-> A(15)
          take :: [A(0) x A(0)] -(0)-> A(0)
          true :: [] -(0)-> A(15)
          true :: [] -(0)-> A(7)
        
        
        Cost-free Signatures used:
        --------------------------
          0 :: [] -(0)-> A_cf(0)
          a__eq :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          a__inf :: [A_cf(0)] -(0)-> A_cf(0)
          a__length :: [A_cf(0)] -(0)-> A_cf(0)
          a__take :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          eq :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          false :: [] -(0)-> A_cf(0)
          inf :: [A_cf(0)] -(0)-> A_cf(0)
          length :: [A_cf(0)] -(0)-> A_cf(0)
          mark :: [A_cf(0)] -(0)-> A_cf(0)
          nil :: [] -(0)-> A_cf(0)
          s :: [A_cf(0)] -(0)-> A_cf(0)
          take :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          true :: [] -(0)-> A_cf(0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1)
          cons_A :: [A(0) x A(1)] -(1)-> A(1)
          eq_A :: [A(1) x A(1)] -(1)-> A(1)
          false_A :: [] -(0)-> A(1)
          inf_A :: [A(1)] -(1)-> A(1)
          length_A :: [A(1)] -(1)-> A(1)
          nil_A :: [] -(0)-> A(1)
          s_A :: [A(1)] -(1)-> A(1)
          take_A :: [A(1) x A(1)] -(1)-> A(1)
          true_A :: [] -(0)-> A(1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        a__eq(X,Y) -> false()
        a__eq(X1,X2) -> eq(X1,X2)
        a__eq(0(),0()) -> true()
        a__eq(s(X),s(Y)) -> a__eq(X,Y)
        a__inf(X) -> cons(X,inf(s(X)))
        a__inf(X) -> inf(X)
        a__length(X) -> length(X)
        a__length(cons(X,L)) -> s(length(L))
        a__length(nil()) -> 0()
        a__take(X1,X2) -> take(X1,X2)
        a__take(0(),X) -> nil()
        a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
        mark(0()) -> 0()
        mark(cons(X1,X2)) -> cons(X1,X2)
        mark(eq(X1,X2)) -> a__eq(X1,X2)
        mark(false()) -> false()
        mark(inf(X)) -> a__inf(mark(X))
        mark(length(X)) -> a__length(mark(X))
        mark(nil()) -> nil()
        mark(s(X)) -> s(X)
        mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
        mark(true()) -> true()
    - Signature:
        {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
        ,true/0}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0
        ,cons,eq,false,inf,length,nil,s,take,true}
Following problems could not be solved:
  - Strict TRS:
      a__eq(X,Y) -> false()
      a__eq(X1,X2) -> eq(X1,X2)
      a__eq(0(),0()) -> true()
      a__eq(s(X),s(Y)) -> a__eq(X,Y)
      a__inf(X) -> cons(X,inf(s(X)))
      a__inf(X) -> inf(X)
      a__length(X) -> length(X)
      a__length(cons(X,L)) -> s(length(L))
      a__length(nil()) -> 0()
      a__take(X1,X2) -> take(X1,X2)
      a__take(0(),X) -> nil()
      a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
      mark(0()) -> 0()
      mark(cons(X1,X2)) -> cons(X1,X2)
      mark(eq(X1,X2)) -> a__eq(X1,X2)
      mark(false()) -> false()
      mark(inf(X)) -> a__inf(mark(X))
      mark(length(X)) -> a__length(mark(X))
      mark(nil()) -> nil()
      mark(s(X)) -> s(X)
      mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
      mark(true()) -> true()
  - Signature:
      {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
      ,true/0}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0
      ,cons,eq,false,inf,length,nil,s,take,true}
WORST_CASE(?,O(n^1))