YES

Problem:
 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)

Proof:
 DP Processor:
  DPs:
   a__tail#(cons(X,XS)) -> mark#(XS)
   mark#(zeros()) -> a__zeros#()
   mark#(tail(X)) -> mark#(X)
   mark#(tail(X)) -> a__tail#(mark(X))
   mark#(cons(X1,X2)) -> mark#(X1)
  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)
  TDG Processor:
   DPs:
    a__tail#(cons(X,XS)) -> mark#(XS)
    mark#(zeros()) -> a__zeros#()
    mark#(tail(X)) -> mark#(X)
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1)
   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)
   graph:
    mark#(tail(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(tail(X)) -> mark#(X) -> mark#(tail(X)) -> a__tail#(mark(X))
    mark#(tail(X)) -> mark#(X) -> mark#(tail(X)) -> mark#(X)
    mark#(tail(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
    mark#(tail(X)) -> a__tail#(mark(X)) ->
    a__tail#(cons(X,XS)) -> mark#(XS)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(tail(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(zeros()) -> a__zeros#()
    a__tail#(cons(X,XS)) -> mark#(XS) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__tail#(cons(X,XS)) -> mark#(XS) ->
    mark#(tail(X)) -> a__tail#(mark(X))
    a__tail#(cons(X,XS)) -> mark#(XS) ->
    mark#(tail(X)) -> mark#(X)
    a__tail#(cons(X,XS)) -> mark#(XS) -> mark#(zeros()) -> a__zeros#()
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 13/25
    DPs:
     mark#(tail(X)) -> mark#(X)
     mark#(tail(X)) -> a__tail#(mark(X))
     a__tail#(cons(X,XS)) -> mark#(XS)
     mark#(cons(X1,X2)) -> mark#(X1)
    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)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [mark#](x0) = x0 + 1,
      
      [a__tail#](x0) = x0 + 1,
      
      [tail](x0) = x0 + 1,
      
      [mark](x0) = x0 + 1,
      
      [a__tail](x0) = x0 + 1,
      
      [cons](x0, x1) = x0 + x1,
      
      [zeros] = 0,
      
      [0] = 1,
      
      [a__zeros] = 1
     orientation:
      mark#(tail(X)) = X + 2 >= X + 1 = mark#(X)
      
      mark#(tail(X)) = X + 2 >= X + 2 = a__tail#(mark(X))
      
      a__tail#(cons(X,XS)) = X + XS + 1 >= XS + 1 = mark#(XS)
      
      mark#(cons(X1,X2)) = X1 + X2 + 1 >= X1 + 1 = mark#(X1)
      
      a__zeros() = 1 >= 1 = cons(0(),zeros())
      
      a__tail(cons(X,XS)) = X + XS + 1 >= XS + 1 = mark(XS)
      
      mark(zeros()) = 1 >= 1 = a__zeros()
      
      mark(tail(X)) = X + 2 >= X + 2 = a__tail(mark(X))
      
      mark(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(mark(X1),X2)
      
      mark(0()) = 2 >= 1 = 0()
      
      a__zeros() = 1 >= 0 = zeros()
      
      a__tail(X) = X + 1 >= X + 1 = tail(X)
     problem:
      DPs:
       mark#(tail(X)) -> a__tail#(mark(X))
       a__tail#(cons(X,XS)) -> mark#(XS)
       mark#(cons(X1,X2)) -> mark#(X1)
      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)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [mark#](x0) = x0,
       
       [a__tail#](x0) = x0,
       
       [tail](x0) = x0 + 1,
       
       [mark](x0) = x0,
       
       [a__tail](x0) = x0 + 1,
       
       [cons](x0, x1) = x0 + x1,
       
       [zeros] = 0,
       
       [0] = 0,
       
       [a__zeros] = 0
      orientation:
       mark#(tail(X)) = X + 1 >= X = a__tail#(mark(X))
       
       a__tail#(cons(X,XS)) = X + XS >= XS = mark#(XS)
       
       mark#(cons(X1,X2)) = X1 + X2 >= X1 = mark#(X1)
       
       a__zeros() = 0 >= 0 = cons(0(),zeros())
       
       a__tail(cons(X,XS)) = X + XS + 1 >= XS = mark(XS)
       
       mark(zeros()) = 0 >= 0 = a__zeros()
       
       mark(tail(X)) = X + 1 >= X + 1 = a__tail(mark(X))
       
       mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = cons(mark(X1),X2)
       
       mark(0()) = 0 >= 0 = 0()
       
       a__zeros() = 0 >= 0 = zeros()
       
       a__tail(X) = X + 1 >= X + 1 = tail(X)
      problem:
       DPs:
        a__tail#(cons(X,XS)) -> mark#(XS)
        mark#(cons(X1,X2)) -> mark#(X1)
       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)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [mark#](x0) = 0,
        
        [a__tail#](x0) = 1,
        
        [tail](x0) = x0 + 1,
        
        [mark](x0) = x0 + 1,
        
        [a__tail](x0) = x0 + 1,
        
        [cons](x0, x1) = x1,
        
        [zeros] = 1,
        
        [0] = 1,
        
        [a__zeros] = 1
       orientation:
        a__tail#(cons(X,XS)) = 1 >= 0 = mark#(XS)
        
        mark#(cons(X1,X2)) = 0 >= 0 = mark#(X1)
        
        a__zeros() = 1 >= 1 = cons(0(),zeros())
        
        a__tail(cons(X,XS)) = XS + 1 >= XS + 1 = mark(XS)
        
        mark(zeros()) = 2 >= 1 = a__zeros()
        
        mark(tail(X)) = X + 2 >= X + 2 = a__tail(mark(X))
        
        mark(cons(X1,X2)) = X2 + 1 >= X2 = cons(mark(X1),X2)
        
        mark(0()) = 2 >= 1 = 0()
        
        a__zeros() = 1 >= 1 = zeros()
        
        a__tail(X) = X + 1 >= X + 1 = tail(X)
       problem:
        DPs:
         mark#(cons(X1,X2)) -> mark#(X1)
        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)
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [mark#](x0) = x0,
         
         [tail](x0) = x0,
         
         [mark](x0) = x0 + 1,
         
         [a__tail](x0) = x0,
         
         [cons](x0, x1) = x0 + x1 + 1,
         
         [zeros] = 0,
         
         [0] = 0,
         
         [a__zeros] = 1
        orientation:
         mark#(cons(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1)
         
         a__zeros() = 1 >= 1 = cons(0(),zeros())
         
         a__tail(cons(X,XS)) = X + XS + 1 >= XS + 1 = mark(XS)
         
         mark(zeros()) = 1 >= 1 = a__zeros()
         
         mark(tail(X)) = X + 1 >= X + 1 = a__tail(mark(X))
         
         mark(cons(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = cons(mark(X1),X2)
         
         mark(0()) = 1 >= 0 = 0()
         
         a__zeros() = 1 >= 0 = zeros()
         
         a__tail(X) = X >= X = tail(X)
        problem:
         DPs:
          
         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)
        Qed