WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          r1(y,z){y -> cons(x,y)} =
            r1(cons(x,y),z) ->^+ r1(y,cons(x,z))
              = C[r1(y,cons(x,z)) = r1(y,z){z -> cons(x,z)}]

** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + 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:
          {r1,rev}
        TcT has computed the following interpretation:
           p(cons) = 2 + x2      
          p(empty) = 0           
             p(r1) = 13*x1 + 8*x2
            p(rev) = 13*x1       
        
        Following rules are strictly oriented:
        r1(cons(x,k),a) = 26 + 8*a + 13*k
                        > 16 + 8*a + 13*k
                        = r1(k,cons(x,a))
        
        
        Following rules are (at-least) weakly oriented:
        r1(empty(),a) =  8*a           
                      >= a             
                      =  a             
        
              rev(ls) =  13*ls         
                      >= 13*ls         
                      =  r1(ls,empty())
        
** Step 1.b:2: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Weak TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + 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:
          {r1,rev}
        TcT has computed the following interpretation:
           p(cons) = [0]         
          p(empty) = [0]         
             p(r1) = [2] x2 + [2]
            p(rev) = [2]         
        
        Following rules are strictly oriented:
        r1(empty(),a) = [2] a + [2]
                      > [1] a + [0]
                      = a          
        
        
        Following rules are (at-least) weakly oriented:
        r1(cons(x,k),a) =  [2] a + [2]    
                        >= [2]            
                        =  r1(k,cons(x,a))
        
                rev(ls) =  [2]            
                        >= [2]            
                        =  r1(ls,empty()) 
        
** Step 1.b:3: NaturalMI WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            rev(ls) -> r1(ls,empty())
        - Weak TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + 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:
          {r1,rev}
        TcT has computed the following interpretation:
           p(cons) = [0]         
          p(empty) = [0]         
             p(r1) = [2] x2 + [0]
            p(rev) = [9]         
        
        Following rules are strictly oriented:
        rev(ls) = [9]           
                > [0]           
                = r1(ls,empty())
        
        
        Following rules are (at-least) weakly oriented:
        r1(cons(x,k),a) =  [2] a + [0]    
                        >= [0]            
                        =  r1(k,cons(x,a))
        
          r1(empty(),a) =  [2] a + [0]    
                        >= [1] a + [0]    
                        =  a              
        
** Step 1.b:4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            r1(cons(x,k),a) -> r1(k,cons(x,a))
            r1(empty(),a) -> a
            rev(ls) -> r1(ls,empty())
        - Signature:
            {r1/2,rev/1} / {cons/2,empty/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {r1,rev} and constructors {cons,empty}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

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