WORST_CASE(?,O(n^1))
* Step 1: Ara WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            comp_f_g#1(plus_x(x3),comp_f_g(x1,x2),0()) -> plus_x#1(x3,comp_f_g#1(x1,x2,0()))
            comp_f_g#1(plus_x(x3),id(),0()) -> plus_x#1(x3,0())
            foldr#3(Cons(x32,x6)) -> comp_f_g(x32,foldr#3(x6))
            foldr#3(Nil()) -> id()
            foldr_f#3(Cons(x16,x5),x24) -> comp_f_g#1(x16,foldr#3(x5),x24)
            foldr_f#3(Nil(),0()) -> 0()
            main(x3) -> foldr_f#3(map#2(x3),0())
            map#2(Cons(x16,x6)) -> Cons(plus_x(x16),map#2(x6))
            map#2(Nil()) -> Nil()
            plus_x#1(0(),x6) -> x6
            plus_x#1(S(x8),x10) -> S(plus_x#1(x8,x10))
        - Signature:
            {comp_f_g#1/3,foldr#3/1,foldr_f#3/2,main/1,map#2/1,plus_x#1/2} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,id/0
            ,plus_x/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {comp_f_g#1,foldr#3,foldr_f#3,main,map#2
            ,plus_x#1} and constructors {0,Cons,Nil,S,comp_f_g,id,plus_x}
    + Applied Processor:
        Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT}
    + Details:
        Signatures used:
        ----------------
          0 :: [] -(0)-> A(0)
          0 :: [] -(0)-> A(1)
          0 :: [] -(0)-> A(2)
          0 :: [] -(0)-> A(5)
          Cons :: [A(3) x A(3)] -(3)-> A(3)
          Cons :: [A(4) x A(4)] -(4)-> A(4)
          Cons :: [A(7) x A(7)] -(7)-> A(7)
          Nil :: [] -(0)-> A(3)
          Nil :: [] -(0)-> A(4)
          Nil :: [] -(0)-> A(7)
          S :: [A(1)] -(1)-> A(1)
          S :: [A(0)] -(0)-> A(0)
          comp_f_g :: [A(2) x A(2)] -(2)-> A(2)
          comp_f_g#1 :: [A(2) x A(2) x A(0)] -(4)-> A(0)
          foldr#3 :: [A(3)] -(2)-> A(2)
          foldr_f#3 :: [A(4) x A(0)] -(5)-> A(0)
          id :: [] -(0)-> A(2)
          main :: [A(7)] -(7)-> A(0)
          map#2 :: [A(7)] -(1)-> A(4)
          plus_x :: [A(2)] -(0)-> A(2)
          plus_x :: [A(4)] -(0)-> A(4)
          plus_x#1 :: [A(1) x A(0)] -(1)-> A(0)
        
        
        Cost-free Signatures used:
        --------------------------
          0 :: [] -(0)-> A_cf(0)
          Cons :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          Nil :: [] -(0)-> A_cf(0)
          S :: [A_cf(0)] -(0)-> A_cf(0)
          comp_f_g :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          comp_f_g#1 :: [A_cf(0) x A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
          foldr#3 :: [A_cf(0)] -(0)-> A_cf(0)
          id :: [] -(0)-> A_cf(0)
          map#2 :: [A_cf(0)] -(0)-> A_cf(0)
          plus_x :: [A_cf(0)] -(0)-> A_cf(0)
          plus_x#1 :: [A_cf(0) x A_cf(0)] -(0)-> A_cf(0)
        
        
        Base Constructor Signatures used:
        ---------------------------------
          0_A :: [] -(0)-> A(1)
          Cons_A :: [A(1) x A(1)] -(1)-> A(1)
          Nil_A :: [] -(0)-> A(1)
          S_A :: [A(1)] -(1)-> A(1)
          comp_f_g_A :: [A(0) x A(0)] -(1)-> A(1)
          id_A :: [] -(0)-> A(1)
          plus_x_A :: [A(0)] -(0)-> A(1)
        
* Step 2: Open MAYBE
    - Strict TRS:
        comp_f_g#1(plus_x(x3),comp_f_g(x1,x2),0()) -> plus_x#1(x3,comp_f_g#1(x1,x2,0()))
        comp_f_g#1(plus_x(x3),id(),0()) -> plus_x#1(x3,0())
        foldr#3(Cons(x32,x6)) -> comp_f_g(x32,foldr#3(x6))
        foldr#3(Nil()) -> id()
        foldr_f#3(Cons(x16,x5),x24) -> comp_f_g#1(x16,foldr#3(x5),x24)
        foldr_f#3(Nil(),0()) -> 0()
        main(x3) -> foldr_f#3(map#2(x3),0())
        map#2(Cons(x16,x6)) -> Cons(plus_x(x16),map#2(x6))
        map#2(Nil()) -> Nil()
        plus_x#1(0(),x6) -> x6
        plus_x#1(S(x8),x10) -> S(plus_x#1(x8,x10))
    - Signature:
        {comp_f_g#1/3,foldr#3/1,foldr_f#3/2,main/1,map#2/1,plus_x#1/2} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,id/0
        ,plus_x/1}
    - Obligation:
        innermost runtime complexity wrt. defined symbols {comp_f_g#1,foldr#3,foldr_f#3,main,map#2
        ,plus_x#1} and constructors {0,Cons,Nil,S,comp_f_g,id,plus_x}
Following problems could not be solved:
  - Strict TRS:
      comp_f_g#1(plus_x(x3),comp_f_g(x1,x2),0()) -> plus_x#1(x3,comp_f_g#1(x1,x2,0()))
      comp_f_g#1(plus_x(x3),id(),0()) -> plus_x#1(x3,0())
      foldr#3(Cons(x32,x6)) -> comp_f_g(x32,foldr#3(x6))
      foldr#3(Nil()) -> id()
      foldr_f#3(Cons(x16,x5),x24) -> comp_f_g#1(x16,foldr#3(x5),x24)
      foldr_f#3(Nil(),0()) -> 0()
      main(x3) -> foldr_f#3(map#2(x3),0())
      map#2(Cons(x16,x6)) -> Cons(plus_x(x16),map#2(x6))
      map#2(Nil()) -> Nil()
      plus_x#1(0(),x6) -> x6
      plus_x#1(S(x8),x10) -> S(plus_x#1(x8,x10))
  - Signature:
      {comp_f_g#1/3,foldr#3/1,foldr_f#3/2,main/1,map#2/1,plus_x#1/2} / {0/0,Cons/2,Nil/0,S/1,comp_f_g/2,id/0
      ,plus_x/1}
  - Obligation:
      innermost runtime complexity wrt. defined symbols {comp_f_g#1,foldr#3,foldr_f#3,main,map#2
      ,plus_x#1} and constructors {0,Cons,Nil,S,comp_f_g,id,plus_x}
WORST_CASE(?,O(n^1))