We consider the following Problem:

  Strict Trs:
    {  a__zeros() -> cons(0(), zeros())
     , a__tail(cons(X, XS)) -> mark(XS)
     , mark(zeros()) -> a__zeros()
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , a__zeros() -> zeros()
     , a__tail(X) -> tail(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  a__zeros() -> cons(0(), zeros())
       , a__tail(cons(X, XS)) -> mark(XS)
       , mark(zeros()) -> a__zeros()
       , mark(tail(X)) -> a__tail(mark(X))
       , mark(cons(X1, X2)) -> cons(mark(X1), X2)
       , mark(0()) -> 0()
       , a__zeros() -> zeros()
       , a__tail(X) -> tail(X)}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component:
      {  a__zeros() -> cons(0(), zeros())
       , mark(0()) -> 0()
       , a__zeros() -> zeros()}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(cons) = {1}, Uargs(a__tail) = {1}, Uargs(mark) = {},
        Uargs(tail) = {}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       a__zeros() = [2]
                    [2]
       cons(x1, x2) = [1 0] x1 + [0 0] x2 + [1]
                      [0 0]      [0 0]      [1]
       0() = [0]
             [0]
       zeros() = [0]
                 [0]
       a__tail(x1) = [1 0] x1 + [0]
                     [0 0]      [1]
       mark(x1) = [0 0] x1 + [1]
                  [0 0]      [1]
       tail(x1) = [0 0] x1 + [0]
                  [0 0]      [0]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs:
        {  a__tail(cons(X, XS)) -> mark(XS)
         , mark(zeros()) -> a__zeros()
         , mark(tail(X)) -> a__tail(mark(X))
         , mark(cons(X1, X2)) -> cons(mark(X1), X2)
         , a__tail(X) -> tail(X)}
      Weak Trs:
        {  a__zeros() -> cons(0(), zeros())
         , mark(0()) -> 0()
         , a__zeros() -> zeros()}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    Proof:
      The weightgap principle applies, where following rules are oriented strictly:
      
      TRS Component:
        {  mark(zeros()) -> a__zeros()
         , a__tail(X) -> tail(X)}
      
      Interpretation of nonconstant growth:
      -------------------------------------
        The following argument positions are usable:
          Uargs(cons) = {1}, Uargs(a__tail) = {1}, Uargs(mark) = {},
          Uargs(tail) = {}
        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
        Interpretation Functions:
         a__zeros() = [0]
                      [1]
         cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                        [0 0]      [0 0]      [1]
         0() = [0]
               [0]
         zeros() = [0]
                   [0]
         a__tail(x1) = [1 0] x1 + [1]
                       [0 0]      [1]
         mark(x1) = [0 0] x1 + [1]
                    [0 0]      [1]
         tail(x1) = [0 0] x1 + [0]
                    [0 0]      [0]
      
      The strictly oriented rules are moved into the weak component.
      
      We consider the following Problem:
      
        Strict Trs:
          {  a__tail(cons(X, XS)) -> mark(XS)
           , mark(tail(X)) -> a__tail(mark(X))
           , mark(cons(X1, X2)) -> cons(mark(X1), X2)}
        Weak Trs:
          {  mark(zeros()) -> a__zeros()
           , a__tail(X) -> tail(X)
           , a__zeros() -> cons(0(), zeros())
           , mark(0()) -> 0()
           , a__zeros() -> zeros()}
        StartTerms: basic terms
        Strategy: innermost
      
      Certificate: YES(?,O(n^1))
      
      Proof:
        The weightgap principle applies, where following rules are oriented strictly:
        
        TRS Component: {a__tail(cons(X, XS)) -> mark(XS)}
        
        Interpretation of nonconstant growth:
        -------------------------------------
          The following argument positions are usable:
            Uargs(cons) = {1}, Uargs(a__tail) = {1}, Uargs(mark) = {},
            Uargs(tail) = {}
          We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
          Interpretation Functions:
           a__zeros() = [0]
                        [0]
           cons(x1, x2) = [1 0] x1 + [0 0] x2 + [0]
                          [0 0]      [0 0]      [0]
           0() = [0]
                 [0]
           zeros() = [0]
                     [0]
           a__tail(x1) = [1 2] x1 + [1]
                         [0 0]      [3]
           mark(x1) = [0 0] x1 + [0]
                      [0 0]      [2]
           tail(x1) = [0 0] x1 + [0]
                      [0 0]      [0]
        
        The strictly oriented rules are moved into the weak component.
        
        We consider the following Problem:
        
          Strict Trs:
            {  mark(tail(X)) -> a__tail(mark(X))
             , mark(cons(X1, X2)) -> cons(mark(X1), X2)}
          Weak Trs:
            {  a__tail(cons(X, XS)) -> mark(XS)
             , mark(zeros()) -> a__zeros()
             , a__tail(X) -> tail(X)
             , a__zeros() -> cons(0(), zeros())
             , mark(0()) -> 0()
             , a__zeros() -> zeros()}
          StartTerms: basic terms
          Strategy: innermost
        
        Certificate: YES(?,O(n^1))
        
        Proof:
          The weightgap principle applies, where following rules are oriented strictly:
          
          TRS Component: {mark(cons(X1, X2)) -> cons(mark(X1), X2)}
          
          Interpretation of nonconstant growth:
          -------------------------------------
            The following argument positions are usable:
              Uargs(cons) = {1}, Uargs(a__tail) = {1}, Uargs(mark) = {},
              Uargs(tail) = {}
            We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
            Interpretation Functions:
             a__zeros() = [0]
                          [1]
             cons(x1, x2) = [1 0] x1 + [0 1] x2 + [0]
                            [0 1]      [0 1]      [1]
             0() = [0]
                   [0]
             zeros() = [0]
                       [0]
             a__tail(x1) = [1 0] x1 + [1]
                           [0 1]      [2]
             mark(x1) = [0 1] x1 + [0]
                        [0 1]      [2]
             tail(x1) = [0 0] x1 + [0]
                        [0 1]      [0]
          
          The strictly oriented rules are moved into the weak component.
          
          We consider the following Problem:
          
            Strict Trs: {mark(tail(X)) -> a__tail(mark(X))}
            Weak Trs:
              {  mark(cons(X1, X2)) -> cons(mark(X1), X2)
               , a__tail(cons(X, XS)) -> mark(XS)
               , mark(zeros()) -> a__zeros()
               , a__tail(X) -> tail(X)
               , a__zeros() -> cons(0(), zeros())
               , mark(0()) -> 0()
               , a__zeros() -> zeros()}
            StartTerms: basic terms
            Strategy: innermost
          
          Certificate: YES(?,O(n^1))
          
          Proof:
            The weightgap principle applies, where following rules are oriented strictly:
            
            TRS Component: {mark(tail(X)) -> a__tail(mark(X))}
            
            Interpretation of nonconstant growth:
            -------------------------------------
              The following argument positions are usable:
                Uargs(cons) = {1}, Uargs(a__tail) = {1}, Uargs(mark) = {},
                Uargs(tail) = {}
              We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
              Interpretation Functions:
               a__zeros() = [0]
                            [0]
               cons(x1, x2) = [1 0] x1 + [0 2] x2 + [0]
                              [0 1]      [0 1]      [0]
               0() = [0]
                     [0]
               zeros() = [0]
                         [0]
               a__tail(x1) = [1 0] x1 + [3]
                             [0 1]      [2]
               mark(x1) = [0 2] x1 + [1]
                          [0 1]      [0]
               tail(x1) = [0 0] x1 + [0]
                          [0 1]      [2]
            
            The strictly oriented rules are moved into the weak component.
            
            We consider the following Problem:
            
              Weak Trs:
                {  mark(tail(X)) -> a__tail(mark(X))
                 , mark(cons(X1, X2)) -> cons(mark(X1), X2)
                 , a__tail(cons(X, XS)) -> mark(XS)
                 , mark(zeros()) -> a__zeros()
                 , a__tail(X) -> tail(X)
                 , a__zeros() -> cons(0(), zeros())
                 , mark(0()) -> 0()
                 , a__zeros() -> zeros()}
              StartTerms: basic terms
              Strategy: innermost
            
            Certificate: YES(O(1),O(1))
            
            Proof:
              We consider the following Problem:
              
                Weak Trs:
                  {  mark(tail(X)) -> a__tail(mark(X))
                   , mark(cons(X1, X2)) -> cons(mark(X1), X2)
                   , a__tail(cons(X, XS)) -> mark(XS)
                   , mark(zeros()) -> a__zeros()
                   , a__tail(X) -> tail(X)
                   , a__zeros() -> cons(0(), zeros())
                   , mark(0()) -> 0()
                   , a__zeros() -> zeros()}
                StartTerms: basic terms
                Strategy: innermost
              
              Certificate: YES(O(1),O(1))
              
              Proof:
                Empty rules are trivially bounded

Hurray, we answered YES(?,O(n^1))