WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,s(c))
            f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
            foldB(t,0()) -> t
            foldB(t,s(n)) -> f(foldB(t,n),B())
            foldC(t,0()) -> t
            foldC(t,s(n)) -> f(foldC(t,n),C())
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f',f'',foldB,foldC,g} and constructors {0,A,B,C,s
            ,triple}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,s(c))
            f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
            foldB(t,0()) -> t
            foldB(t,s(n)) -> f(foldB(t,n),B())
            foldC(t,0()) -> t
            foldC(t,s(n)) -> f(foldC(t,n),C())
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f',f'',foldB,foldC,g} and constructors {0,A,B,C,s
            ,triple}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,s(c))
            f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
            foldB(t,0()) -> t
            foldB(t,s(n)) -> f(foldB(t,n),B())
            foldC(t,0()) -> t
            foldC(t,s(n)) -> f(foldC(t,n),C())
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f',f'',foldB,foldC,g} and constructors {0,A,B,C,s
            ,triple}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "A") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "A") :: [] -(0)-> "A"(0, 0, 1)
          F (TrsFun "B") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "B") :: [] -(0)-> "A"(0, 0, 1)
          F (TrsFun "C") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "C") :: [] -(0)-> "A"(0, 0, 1)
          F (TrsFun "f") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "f'") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "f''") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "foldB") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "foldC") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "g") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "triple") :: ["A"(0, 0, 0) x "A"(0, 0, 0) x "A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(t,x) -> f'(t,g(x))
          f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
          f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
          f'(triple(a,b,c),C()) -> triple(a,b,s(c))
          f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
          foldB(t,0()) -> t
          foldB(t,s(n)) -> f(foldB(t,n),B())
          foldC(t,0()) -> t
          foldC(t,s(n)) -> f(foldC(t,n),C())
          g(A()) -> A()
          g(B()) -> A()
          g(B()) -> B()
          g(C()) -> A()
          g(C()) -> B()
          g(C()) -> C()
          main(x1) -> g(x1)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(t,x) -> f'(t,g(x))
            f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
            f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
            f'(triple(a,b,c),C()) -> triple(a,b,s(c))
            f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
            foldB(t,0()) -> t
            foldB(t,s(n)) -> f(foldB(t,n),B())
            foldC(t,0()) -> t
            foldC(t,s(n)) -> f(foldC(t,n),C())
            g(A()) -> A()
            g(B()) -> A()
            g(B()) -> B()
            g(C()) -> A()
            g(C()) -> B()
            g(C()) -> C()
        - Signature:
            {f/2,f'/2,f''/1,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,f',f'',foldB,foldC,g} and constructors {0,A,B,C,s
            ,triple}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          foldB(x,y){y -> s(y)} =
            foldB(x,s(y)) ->^+ f(foldB(x,y),B())
              = C[foldB(x,y) = foldB(x,y){}]

WORST_CASE(Omega(n^1),?)