* Step 1: Sum WORST_CASE(Omega(n^1),O(n^3))
    + Considered Problem:
        - Strict TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> cons(x,y)} =
            mark(cons(x,y)) ->^+ cons(mark(x),y)
              = C[mark(x) = mark(x){}]

** Step 1.b:1: WeightGap WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,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(a__from) = {1},
            uargs(cons) = {1},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                     p(0) = [11]        
               p(a__from) = [1] x1 + [1]
             p(a__length) = [0]         
            p(a__length1) = [0]         
                  p(cons) = [1] x1 + [0]
                  p(from) = [1] x1 + [0]
                p(length) = [0]         
               p(length1) = [0]         
                  p(mark) = [1] x1 + [0]
                   p(nil) = [0]         
                     p(s) = [1] x1 + [0]
          
          Following rules are strictly oriented:
          a__from(X) = [1] X + [1]             
                     > [1] X + [0]             
                     = cons(mark(X),from(s(X)))
          
          a__from(X) = [1] X + [1]             
                     > [1] X + [0]             
                     = from(X)                 
          
          
          Following rules are (at-least) weakly oriented:
                  a__length(X) =  [0]              
                               >= [0]              
                               =  length(X)        
          
          a__length(cons(X,Y)) =  [0]              
                               >= [0]              
                               =  s(a__length1(Y)) 
          
              a__length(nil()) =  [0]              
                               >= [11]             
                               =  0()              
          
                 a__length1(X) =  [0]              
                               >= [0]              
                               =  a__length(X)     
          
                 a__length1(X) =  [0]              
                               >= [0]              
                               =  length1(X)       
          
                     mark(0()) =  [11]             
                               >= [11]             
                               =  0()              
          
             mark(cons(X1,X2)) =  [1] X1 + [0]     
                               >= [1] X1 + [0]     
                               =  cons(mark(X1),X2)
          
                 mark(from(X)) =  [1] X + [0]      
                               >= [1] X + [1]      
                               =  a__from(mark(X)) 
          
               mark(length(X)) =  [0]              
                               >= [0]              
                               =  a__length(X)     
          
              mark(length1(X)) =  [0]              
                               >= [0]              
                               =  a__length1(X)    
          
                   mark(nil()) =  [0]              
                               >= [0]              
                               =  nil()            
          
                    mark(s(X)) =  [1] X + [0]      
                               >= [1] X + [0]      
                               =  s(mark(X))       
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 1.b:2: WeightGap WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,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(a__from) = {1},
            uargs(cons) = {1},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                     p(0) = [0]         
               p(a__from) = [1] x1 + [1]
             p(a__length) = [7]         
            p(a__length1) = [0]         
                  p(cons) = [1] x1 + [1]
                  p(from) = [1] x1 + [1]
                p(length) = [9]         
               p(length1) = [0]         
                  p(mark) = [1] x1 + [0]
                   p(nil) = [0]         
                     p(s) = [1] x1 + [9]
          
          Following rules are strictly oriented:
          a__length(nil()) = [7]         
                           > [0]         
                           = 0()         
          
           mark(length(X)) = [9]         
                           > [7]         
                           = a__length(X)
          
          
          Following rules are (at-least) weakly oriented:
                    a__from(X) =  [1] X + [1]             
                               >= [1] X + [1]             
                               =  cons(mark(X),from(s(X)))
          
                    a__from(X) =  [1] X + [1]             
                               >= [1] X + [1]             
                               =  from(X)                 
          
                  a__length(X) =  [7]                     
                               >= [9]                     
                               =  length(X)               
          
          a__length(cons(X,Y)) =  [7]                     
                               >= [9]                     
                               =  s(a__length1(Y))        
          
                 a__length1(X) =  [0]                     
                               >= [7]                     
                               =  a__length(X)            
          
                 a__length1(X) =  [0]                     
                               >= [0]                     
                               =  length1(X)              
          
                     mark(0()) =  [0]                     
                               >= [0]                     
                               =  0()                     
          
             mark(cons(X1,X2)) =  [1] X1 + [1]            
                               >= [1] X1 + [1]            
                               =  cons(mark(X1),X2)       
          
                 mark(from(X)) =  [1] X + [1]             
                               >= [1] X + [1]             
                               =  a__from(mark(X))        
          
              mark(length1(X)) =  [0]                     
                               >= [0]                     
                               =  a__length1(X)           
          
                   mark(nil()) =  [0]                     
                               >= [0]                     
                               =  nil()                   
          
                    mark(s(X)) =  [1] X + [9]             
                               >= [1] X + [9]             
                               =  s(mark(X))              
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 1.b:3: WeightGap WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(nil()) -> 0()
            mark(length(X)) -> a__length(X)
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,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(a__from) = {1},
            uargs(cons) = {1},
            uargs(s) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                     p(0) = [6]         
               p(a__from) = [1] x1 + [9]
             p(a__length) = [6]         
            p(a__length1) = [0]         
                  p(cons) = [1] x1 + [4]
                  p(from) = [1] x1 + [9]
                p(length) = [1]         
               p(length1) = [0]         
                  p(mark) = [1] x1 + [5]
                   p(nil) = [0]         
                     p(s) = [1] x1 + [0]
          
          Following rules are strictly oriented:
                  a__length(X) = [6]             
                               > [1]             
                               = length(X)       
          
          a__length(cons(X,Y)) = [6]             
                               > [0]             
                               = s(a__length1(Y))
          
                     mark(0()) = [11]            
                               > [6]             
                               = 0()             
          
              mark(length1(X)) = [5]             
                               > [0]             
                               = a__length1(X)   
          
                   mark(nil()) = [5]             
                               > [0]             
                               = nil()           
          
          
          Following rules are (at-least) weakly oriented:
                 a__from(X) =  [1] X + [9]             
                            >= [1] X + [9]             
                            =  cons(mark(X),from(s(X)))
          
                 a__from(X) =  [1] X + [9]             
                            >= [1] X + [9]             
                            =  from(X)                 
          
           a__length(nil()) =  [6]                     
                            >= [6]                     
                            =  0()                     
          
              a__length1(X) =  [0]                     
                            >= [6]                     
                            =  a__length(X)            
          
              a__length1(X) =  [0]                     
                            >= [0]                     
                            =  length1(X)              
          
          mark(cons(X1,X2)) =  [1] X1 + [9]            
                            >= [1] X1 + [9]            
                            =  cons(mark(X1),X2)       
          
              mark(from(X)) =  [1] X + [14]            
                            >= [1] X + [14]            
                            =  a__from(mark(X))        
          
            mark(length(X)) =  [6]                     
                            >= [6]                     
                            =  a__length(X)            
          
                 mark(s(X)) =  [1] X + [5]             
                            >= [1] X + [5]             
                            =  s(mark(X))              
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 1.b:4: MI WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            mark(0()) -> 0()
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          uargs(a__from) = {1},
          uargs(cons) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {a__from,a__length,a__length1,mark}
        TcT has computed the following interpretation:
                   p(0) = [0]          
             p(a__from) = [1] x_1 + [3]
           p(a__length) = [1]          
          p(a__length1) = [1]          
                p(cons) = [1] x_1 + [1]
                p(from) = [1] x_1 + [3]
              p(length) = [1]          
             p(length1) = [0]          
                p(mark) = [1] x_1 + [1]
                 p(nil) = [1]          
                   p(s) = [1] x_1 + [0]
        
        Following rules are strictly oriented:
        a__length1(X) = [1]       
                      > [0]       
                      = length1(X)
        
        
        Following rules are (at-least) weakly oriented:
                  a__from(X) =  [1] X + [3]             
                             >= [1] X + [2]             
                             =  cons(mark(X),from(s(X)))
        
                  a__from(X) =  [1] X + [3]             
                             >= [1] X + [3]             
                             =  from(X)                 
        
                a__length(X) =  [1]                     
                             >= [1]                     
                             =  length(X)               
        
        a__length(cons(X,Y)) =  [1]                     
                             >= [1]                     
                             =  s(a__length1(Y))        
        
            a__length(nil()) =  [1]                     
                             >= [0]                     
                             =  0()                     
        
               a__length1(X) =  [1]                     
                             >= [1]                     
                             =  a__length(X)            
        
                   mark(0()) =  [1]                     
                             >= [0]                     
                             =  0()                     
        
           mark(cons(X1,X2)) =  [1] X1 + [2]            
                             >= [1] X1 + [2]            
                             =  cons(mark(X1),X2)       
        
               mark(from(X)) =  [1] X + [4]             
                             >= [1] X + [4]             
                             =  a__from(mark(X))        
        
             mark(length(X)) =  [2]                     
                             >= [1]                     
                             =  a__length(X)            
        
            mark(length1(X)) =  [1]                     
                             >= [1]                     
                             =  a__length1(X)           
        
                 mark(nil()) =  [2]                     
                             >= [1]                     
                             =  nil()                   
        
                  mark(s(X)) =  [1] X + [1]             
                             >= [1] X + [1]             
                             =  s(mark(X))              
        
** Step 1.b:5: MI WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            a__length1(X) -> a__length(X)
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          uargs(a__from) = {1},
          uargs(cons) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {a__from,a__length,a__length1,mark}
        TcT has computed the following interpretation:
                   p(0) = [4]                        
                          [0]                        
             p(a__from) = [1 0] x_1 + [4]            
                          [0 0]       [3]            
           p(a__length) = [0 3] x_1 + [0]            
                          [0 0]       [0]            
          p(a__length1) = [0 3] x_1 + [3]            
                          [0 0]       [0]            
                p(cons) = [1 0] x_1 + [0 0] x_2 + [0]
                          [0 0]       [0 1]       [1]
                p(from) = [1 0] x_1 + [4]            
                          [0 0]       [2]            
              p(length) = [0 3] x_1 + [0]            
                          [0 0]       [0]            
             p(length1) = [0 3] x_1 + [0]            
                          [0 0]       [0]            
                p(mark) = [1 0] x_1 + [4]            
                          [0 2]       [0]            
                 p(nil) = [4]                        
                          [4]                        
                   p(s) = [1 0] x_1 + [0]            
                          [0 0]       [0]            
        
        Following rules are strictly oriented:
        a__length1(X) = [0 3] X + [3]
                        [0 0]     [0]
                      > [0 3] X + [0]
                        [0 0]     [0]
                      = a__length(X) 
        
        
        Following rules are (at-least) weakly oriented:
                  a__from(X) =  [1 0] X + [4]            
                                [0 0]     [3]            
                             >= [1 0] X + [4]            
                                [0 0]     [3]            
                             =  cons(mark(X),from(s(X))) 
        
                  a__from(X) =  [1 0] X + [4]            
                                [0 0]     [3]            
                             >= [1 0] X + [4]            
                                [0 0]     [2]            
                             =  from(X)                  
        
                a__length(X) =  [0 3] X + [0]            
                                [0 0]     [0]            
                             >= [0 3] X + [0]            
                                [0 0]     [0]            
                             =  length(X)                
        
        a__length(cons(X,Y)) =  [0 3] Y + [3]            
                                [0 0]     [0]            
                             >= [0 3] Y + [3]            
                                [0 0]     [0]            
                             =  s(a__length1(Y))         
        
            a__length(nil()) =  [12]                     
                                [0]                      
                             >= [4]                      
                                [0]                      
                             =  0()                      
        
               a__length1(X) =  [0 3] X + [3]            
                                [0 0]     [0]            
                             >= [0 3] X + [0]            
                                [0 0]     [0]            
                             =  length1(X)               
        
                   mark(0()) =  [8]                      
                                [0]                      
                             >= [4]                      
                                [0]                      
                             =  0()                      
        
           mark(cons(X1,X2)) =  [1 0] X1 + [0 0] X2 + [4]
                                [0 0]      [0 2]      [2]
                             >= [1 0] X1 + [0 0] X2 + [4]
                                [0 0]      [0 1]      [1]
                             =  cons(mark(X1),X2)        
        
               mark(from(X)) =  [1 0] X + [8]            
                                [0 0]     [4]            
                             >= [1 0] X + [8]            
                                [0 0]     [3]            
                             =  a__from(mark(X))         
        
             mark(length(X)) =  [0 3] X + [4]            
                                [0 0]     [0]            
                             >= [0 3] X + [0]            
                                [0 0]     [0]            
                             =  a__length(X)             
        
            mark(length1(X)) =  [0 3] X + [4]            
                                [0 0]     [0]            
                             >= [0 3] X + [3]            
                                [0 0]     [0]            
                             =  a__length1(X)            
        
                 mark(nil()) =  [8]                      
                                [8]                      
                             >= [4]                      
                                [4]                      
                             =  nil()                    
        
                  mark(s(X)) =  [1 0] X + [4]            
                                [0 0]     [0]            
                             >= [1 0] X + [4]            
                                [0 0]     [0]            
                             =  s(mark(X))               
        
** Step 1.b:6: MI WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          uargs(a__from) = {1},
          uargs(cons) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {a__from,a__length,a__length1,mark}
        TcT has computed the following interpretation:
                   p(0) = [0]            
                          [0]            
             p(a__from) = [1 4] x_1 + [0]
                          [0 1]       [1]
           p(a__length) = [0]            
                          [0]            
          p(a__length1) = [0]            
                          [0]            
                p(cons) = [1 0] x_1 + [0]
                          [0 1]       [1]
                p(from) = [1 4] x_1 + [0]
                          [0 1]       [1]
              p(length) = [0]            
                          [0]            
             p(length1) = [0]            
                          [0]            
                p(mark) = [1 4] x_1 + [0]
                          [0 1]       [0]
                 p(nil) = [0]            
                          [0]            
                   p(s) = [1 0] x_1 + [0]
                          [0 1]       [0]
        
        Following rules are strictly oriented:
        mark(cons(X1,X2)) = [1 4] X1 + [4]   
                            [0 1]      [1]   
                          > [1 4] X1 + [0]   
                            [0 1]      [1]   
                          = cons(mark(X1),X2)
        
            mark(from(X)) = [1 8] X + [4]    
                            [0 1]     [1]    
                          > [1 8] X + [0]    
                            [0 1]     [1]    
                          = a__from(mark(X)) 
        
        
        Following rules are (at-least) weakly oriented:
                  a__from(X) =  [1 4] X + [0]           
                                [0 1]     [1]           
                             >= [1 4] X + [0]           
                                [0 1]     [1]           
                             =  cons(mark(X),from(s(X)))
        
                  a__from(X) =  [1 4] X + [0]           
                                [0 1]     [1]           
                             >= [1 4] X + [0]           
                                [0 1]     [1]           
                             =  from(X)                 
        
                a__length(X) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  length(X)               
        
        a__length(cons(X,Y)) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  s(a__length1(Y))        
        
            a__length(nil()) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  0()                     
        
               a__length1(X) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  a__length(X)            
        
               a__length1(X) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  length1(X)              
        
                   mark(0()) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  0()                     
        
             mark(length(X)) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  a__length(X)            
        
            mark(length1(X)) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  a__length1(X)           
        
                 mark(nil()) =  [0]                     
                                [0]                     
                             >= [0]                     
                                [0]                     
                             =  nil()                   
        
                  mark(s(X)) =  [1 4] X + [0]           
                                [0 1]     [0]           
                             >= [1 4] X + [0]           
                                [0 1]     [0]           
                             =  s(mark(X))              
        
** Step 1.b:7: MI WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            mark(s(X)) -> s(mark(X))
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 3, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):
        
        The following argument positions are considered usable:
          uargs(a__from) = {1},
          uargs(cons) = {1},
          uargs(s) = {1}
        
        Following symbols are considered usable:
          {a__from,a__length,a__length1,mark}
        TcT has computed the following interpretation:
                   p(0) = [1]                            
                          [1]                            
                          [0]                            
             p(a__from) = [1 2 0]       [4]              
                          [0 1 0] x_1 + [0]              
                          [1 2 0]       [5]              
           p(a__length) = [0 0 0]       [1]              
                          [0 0 2] x_1 + [4]              
                          [0 0 0]       [0]              
          p(a__length1) = [0 0 0]       [1]              
                          [0 0 2] x_1 + [4]              
                          [0 0 0]       [0]              
                p(cons) = [1 0 0]       [0 0 1]       [2]
                          [0 1 0] x_1 + [0 0 0] x_2 + [0]
                          [0 0 0]       [0 0 1]       [2]
                p(from) = [1 2 0]       [4]              
                          [0 1 0] x_1 + [0]              
                          [0 0 0]       [0]              
              p(length) = [0 0 0]       [0]              
                          [0 0 2] x_1 + [4]              
                          [0 0 0]       [0]              
             p(length1) = [0 0 0]       [0]              
                          [0 0 2] x_1 + [4]              
                          [0 0 0]       [0]              
                p(mark) = [1 2 0]       [2]              
                          [0 1 0] x_1 + [0]              
                          [2 0 0]       [0]              
                 p(nil) = [1]                            
                          [0]                            
                          [2]                            
                   p(s) = [1 0 0]       [0]              
                          [0 1 0] x_1 + [2]              
                          [0 0 0]       [0]              
        
        Following rules are strictly oriented:
        mark(s(X)) = [1 2 0]     [6]
                     [0 1 0] X + [2]
                     [2 0 0]     [0]
                   > [1 2 0]     [2]
                     [0 1 0] X + [2]
                     [0 0 0]     [0]
                   = s(mark(X))     
        
        
        Following rules are (at-least) weakly oriented:
                  a__from(X) =  [1 2 0]     [4]              
                                [0 1 0] X + [0]              
                                [1 2 0]     [5]              
                             >= [1 2 0]     [4]              
                                [0 1 0] X + [0]              
                                [0 0 0]     [2]              
                             =  cons(mark(X),from(s(X)))     
        
                  a__from(X) =  [1 2 0]     [4]              
                                [0 1 0] X + [0]              
                                [1 2 0]     [5]              
                             >= [1 2 0]     [4]              
                                [0 1 0] X + [0]              
                                [0 0 0]     [0]              
                             =  from(X)                      
        
                a__length(X) =  [0 0 0]     [1]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             >= [0 0 0]     [0]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             =  length(X)                    
        
        a__length(cons(X,Y)) =  [0 0 0]     [1]              
                                [0 0 2] Y + [8]              
                                [0 0 0]     [0]              
                             >= [0 0 0]     [1]              
                                [0 0 2] Y + [6]              
                                [0 0 0]     [0]              
                             =  s(a__length1(Y))             
        
            a__length(nil()) =  [1]                          
                                [8]                          
                                [0]                          
                             >= [1]                          
                                [1]                          
                                [0]                          
                             =  0()                          
        
               a__length1(X) =  [0 0 0]     [1]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             >= [0 0 0]     [1]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             =  a__length(X)                 
        
               a__length1(X) =  [0 0 0]     [1]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             >= [0 0 0]     [0]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             =  length1(X)                   
        
                   mark(0()) =  [5]                          
                                [1]                          
                                [2]                          
                             >= [1]                          
                                [1]                          
                                [0]                          
                             =  0()                          
        
           mark(cons(X1,X2)) =  [1 2 0]      [0 0 1]      [4]
                                [0 1 0] X1 + [0 0 0] X2 + [0]
                                [2 0 0]      [0 0 2]      [4]
                             >= [1 2 0]      [0 0 1]      [4]
                                [0 1 0] X1 + [0 0 0] X2 + [0]
                                [0 0 0]      [0 0 1]      [2]
                             =  cons(mark(X1),X2)            
        
               mark(from(X)) =  [1 4 0]     [6]              
                                [0 1 0] X + [0]              
                                [2 4 0]     [8]              
                             >= [1 4 0]     [6]              
                                [0 1 0] X + [0]              
                                [1 4 0]     [7]              
                             =  a__from(mark(X))             
        
             mark(length(X)) =  [0 0 4]     [10]             
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             >= [0 0 0]     [1]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             =  a__length(X)                 
        
            mark(length1(X)) =  [0 0 4]     [10]             
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             >= [0 0 0]     [1]              
                                [0 0 2] X + [4]              
                                [0 0 0]     [0]              
                             =  a__length1(X)                
        
                 mark(nil()) =  [3]                          
                                [0]                          
                                [2]                          
                             >= [1]                          
                                [0]                          
                                [2]                          
                             =  nil()                        
        
** Step 1.b:8: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__length(X) -> length(X)
            a__length(cons(X,Y)) -> s(a__length1(Y))
            a__length(nil()) -> 0()
            a__length1(X) -> a__length(X)
            a__length1(X) -> length1(X)
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(length(X)) -> a__length(X)
            mark(length1(X)) -> a__length1(X)
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__from/1,a__length/1,a__length1/1,mark/1} / {0/0,cons/2,from/1,length/1,length1/1,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__from,a__length,a__length1,mark} and constructors {0
            ,cons,from,length,length1,nil,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^3))