WORST_CASE(?,O(n^1))
* Step 1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            main(x,y) -> minus(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {main/2,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,minus} 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:
          none
        
        Following symbols are considered usable:
          {main,minus}
        TcT has computed the following interpretation:
              p(0) = [0]         
           p(main) = [8] x1 + [8]
          p(minus) = [8] x1 + [0]
              p(s) = [1] x1 + [0]
        
        Following rules are strictly oriented:
        main(x,y) = [8] x + [8]
                  > [8] x + [0]
                  = minus(x,y) 
        
        
        Following rules are (at-least) weakly oriented:
            minus(x,0()) =  [8] x + [0]
                         >= [1] x + [0]
                         =  x          
        
        minus(s(x),s(y)) =  [8] x + [0]
                         >= [8] x + [0]
                         =  minus(x,y) 
        
* Step 2: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Weak TRS:
            main(x,y) -> minus(x,y)
        - Signature:
            {main/2,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,minus} and constructors {0,s}
    + 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:
          none
        
        Following symbols are considered usable:
          {main,minus}
        TcT has computed the following interpretation:
              p(0) = 0       
           p(main) = 5 + 8*x1
          p(minus) = 5 + 8*x1
              p(s) = x1      
        
        Following rules are strictly oriented:
        minus(x,0()) = 5 + 8*x
                     > x      
                     = x      
        
        
        Following rules are (at-least) weakly oriented:
               main(x,y) =  5 + 8*x   
                         >= 5 + 8*x   
                         =  minus(x,y)
        
        minus(s(x),s(y)) =  5 + 8*x   
                         >= 5 + 8*x   
                         =  minus(x,y)
        
* Step 3: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            minus(s(x),s(y)) -> minus(x,y)
        - Weak TRS:
            main(x,y) -> minus(x,y)
            minus(x,0()) -> x
        - Signature:
            {main/2,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,minus} and constructors {0,s}
    + 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:
          none
        
        Following symbols are considered usable:
          {main,minus}
        TcT has computed the following interpretation:
              p(0) = 0         
           p(main) = 12*x1 + x2
          p(minus) = 12*x1 + x2
              p(s) = 1 + x1    
        
        Following rules are strictly oriented:
        minus(s(x),s(y)) = 13 + 12*x + y
                         > 12*x + y     
                         = minus(x,y)   
        
        
        Following rules are (at-least) weakly oriented:
           main(x,y) =  12*x + y  
                     >= 12*x + y  
                     =  minus(x,y)
        
        minus(x,0()) =  12*x      
                     >= x         
                     =  x         
        
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            main(x,y) -> minus(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {main/2,minus/2} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {main,minus} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))