WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            minus(X,0()) -> X
            minus(s(X),s(Y)) -> p(minus(X,Y))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, 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:
        The following argument positions are considered usable:
          uargs(div) = {1},
          uargs(p) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {div,minus,p}
        TcT has computed the following interpretation:
              p(0) = [2]         
            p(div) = [8] x1 + [2]
          p(minus) = [1] x1 + [0]
              p(p) = [1] x1 + [2]
              p(s) = [1] x1 + [2]
        
        Following rules are strictly oriented:
         div(0(),s(Y)) = [18]                   
                       > [2]                    
                       = 0()                    
        
        div(s(X),s(Y)) = [8] X + [18]           
                       > [8] X + [4]            
                       = s(div(minus(X,Y),s(Y)))
        
               p(s(X)) = [1] X + [4]            
                       > [1] X + [0]            
                       = X                      
        
        
        Following rules are (at-least) weakly oriented:
            minus(X,0()) =  [1] X + [0]  
                         >= [1] X + [0]  
                         =  X            
        
        minus(s(X),s(Y)) =  [1] X + [2]  
                         >= [1] X + [2]  
                         =  p(minus(X,Y))
        
* Step 2: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(X,0()) -> X
            minus(s(X),s(Y)) -> p(minus(X,Y))
        - Weak TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,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(div) = {1},
            uargs(p) = {1},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                p(0) = [0]         
              p(div) = [1] x1 + [0]
            p(minus) = [1] x1 + [0]
                p(p) = [1] x1 + [0]
                p(s) = [1] x1 + [1]
          
          Following rules are strictly oriented:
          minus(s(X),s(Y)) = [1] X + [1]  
                           > [1] X + [0]  
                           = p(minus(X,Y))
          
          
          Following rules are (at-least) weakly oriented:
           div(0(),s(Y)) =  [0]                    
                         >= [0]                    
                         =  0()                    
          
          div(s(X),s(Y)) =  [1] X + [1]            
                         >= [1] X + [1]            
                         =  s(div(minus(X,Y),s(Y)))
          
            minus(X,0()) =  [1] X + [0]            
                         >= [1] X + [0]            
                         =  X                      
          
                 p(s(X)) =  [1] X + [1]            
                         >= [1] X + [0]            
                         =  X                      
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(X,0()) -> X
        - Weak TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            minus(s(X),s(Y)) -> p(minus(X,Y))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, 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:
        The following argument positions are considered usable:
          uargs(div) = {1},
          uargs(p) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {div,minus,p}
        TcT has computed the following interpretation:
              p(0) = [2]         
            p(div) = [8] x1 + [5]
          p(minus) = [1] x1 + [2]
              p(p) = [1] x1 + [0]
              p(s) = [1] x1 + [3]
        
        Following rules are strictly oriented:
        minus(X,0()) = [1] X + [2]
                     > [1] X + [0]
                     = X          
        
        
        Following rules are (at-least) weakly oriented:
           div(0(),s(Y)) =  [21]                   
                         >= [2]                    
                         =  0()                    
        
          div(s(X),s(Y)) =  [8] X + [29]           
                         >= [8] X + [24]           
                         =  s(div(minus(X,Y),s(Y)))
        
        minus(s(X),s(Y)) =  [1] X + [5]            
                         >= [1] X + [2]            
                         =  p(minus(X,Y))          
        
                 p(s(X)) =  [1] X + [3]            
                         >= [1] X + [0]            
                         =  X                      
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            div(0(),s(Y)) -> 0()
            div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))
            minus(X,0()) -> X
            minus(s(X),s(Y)) -> p(minus(X,Y))
            p(s(X)) -> X
        - Signature:
            {div/2,minus/2,p/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))