WORST_CASE(?,O(n^1))
* Step 1: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
            times(X,s(Y)) -> plus(X,times(Y,X))
        - Signature:
            {plus/2,times/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {plus,times} and constructors {s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following nonconstant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(plus) = {2}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
             p(plus) = [1] x2 + [0]         
                p(s) = [1] x1 + [1]         
            p(times) = [1] x1 + [1] x2 + [8]
          
          Following rules are strictly oriented:
          times(X,s(Y)) = [1] X + [1] Y + [9]
                        > [1] X + [1] Y + [8]
                        = plus(X,times(Y,X)) 
          
          
          Following rules are (at-least) weakly oriented:
          plus(plus(X,Y),Z) =  [1] Z + [0]      
                            >= [1] Z + [0]      
                            =  plus(X,plus(Y,Z))
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
        - Weak TRS:
            times(X,s(Y)) -> plus(X,times(Y,X))
        - Signature:
            {plus/2,times/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {plus,times} and constructors {s}
    + Applied Processor:
        NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima):
        The following argument positions are considered usable:
          uargs(plus) = {2}
        
        Following symbols are considered usable:
          {plus,times}
        TcT has computed the following interpretation:
           p(plus) = [0 1] x1 + [1 0] x2 + [0]
                     [0 2]      [0 1]      [1]
              p(s) = [1 1] x1 + [2]           
                     [0 0]      [1]           
          p(times) = [1 1] x1 + [1 0] x2 + [6]
                     [2 2]      [2 0]      [4]
        
        Following rules are strictly oriented:
        plus(plus(X,Y),Z) = [0 2] X + [0 1] Y + [1 0] Z + [1]
                            [0 4]     [0 2]     [0 1]     [3]
                          > [0 1] X + [0 1] Y + [1 0] Z + [0]
                            [0 2]     [0 2]     [0 1]     [2]
                          = plus(X,plus(Y,Z))                
        
        
        Following rules are (at-least) weakly oriented:
        times(X,s(Y)) =  [1 1] X + [1 1] Y + [8]
                         [2 2]     [2 2]     [8]
                      >= [1 1] X + [1 1] Y + [6]
                         [2 2]     [2 2]     [5]
                      =  plus(X,times(Y,X))     
        
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            plus(plus(X,Y),Z) -> plus(X,plus(Y,Z))
            times(X,s(Y)) -> plus(X,times(Y,X))
        - Signature:
            {plus/2,times/2} / {s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {plus,times} and constructors {s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))