WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            and(tt(),X) -> activate(X)
            plus(N,0()) -> N
            plus(N,s(M)) -> s(plus(N,M))
        - Signature:
            {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            and(tt(),X) -> activate(X)
            plus(N,0()) -> N
            plus(N,s(M)) -> s(plus(N,M))
        - Signature:
            {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          plus(x,y){y -> s(y)} =
            plus(x,s(y)) ->^+ s(plus(x,y))
              = C[plus(x,y) = plus(x,y){}]

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            and(tt(),X) -> activate(X)
            plus(N,0()) -> N
            plus(N,s(M)) -> s(plus(N,M))
        - Signature:
            {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
    + Applied Processor:
        NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a polynomial interpretation of kind constructor-based(linear):
        The following argument positions are considered usable:
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {activate,and,plus}
        TcT has computed the following interpretation:
                 p(0) = 1              
          p(activate) = 1 + 8*x1       
               p(and) = 4 + 2*x1 + 8*x2
              p(plus) = 1 + x1 + 2*x2  
                 p(s) = 8 + x1         
                p(tt) = 2              
        
        Following rules are strictly oriented:
         activate(X) = 1 + 8*X     
                     > X           
                     = X           
        
         and(tt(),X) = 8 + 8*X     
                     > 1 + 8*X     
                     = activate(X) 
        
         plus(N,0()) = 3 + N       
                     > N           
                     = N           
        
        plus(N,s(M)) = 17 + 2*M + N
                     > 9 + 2*M + N 
                     = s(plus(N,M))
        
        
        Following rules are (at-least) weakly oriented:
        
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            activate(X) -> X
            and(tt(),X) -> activate(X)
            plus(N,0()) -> N
            plus(N,s(M)) -> s(plus(N,M))
        - Signature:
            {activate/1,and/2,plus/2} / {0/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,and,plus} and constructors {0,s,tt}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))