YES

Problem:
 a__from(X) -> cons(mark(X),from(s(X)))
 a__length(nil()) -> 0()
 a__length(cons(X,Y)) -> s(a__length1(Y))
 a__length1(X) -> a__length(X)
 mark(from(X)) -> a__from(mark(X))
 mark(length(X)) -> a__length(X)
 mark(length1(X)) -> a__length1(X)
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 mark(nil()) -> nil()
 mark(0()) -> 0()
 a__from(X) -> from(X)
 a__length(X) -> length(X)
 a__length1(X) -> length1(X)

Proof:
 DP Processor:
  DPs:
   a__from#(X) -> mark#(X)
   a__length#(cons(X,Y)) -> a__length1#(Y)
   a__length1#(X) -> a__length#(X)
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(length(X)) -> a__length#(X)
   mark#(length1(X)) -> a__length1#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__from(X) -> cons(mark(X),from(s(X)))
   a__length(nil()) -> 0()
   a__length(cons(X,Y)) -> s(a__length1(Y))
   a__length1(X) -> a__length(X)
   mark(from(X)) -> a__from(mark(X))
   mark(length(X)) -> a__length(X)
   mark(length1(X)) -> a__length1(X)
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   mark(nil()) -> nil()
   mark(0()) -> 0()
   a__from(X) -> from(X)
   a__length(X) -> length(X)
   a__length1(X) -> length1(X)
  TDG Processor:
   DPs:
    a__from#(X) -> mark#(X)
    a__length#(cons(X,Y)) -> a__length1#(Y)
    a__length1#(X) -> a__length#(X)
    mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X))
    mark#(length(X)) -> a__length#(X)
    mark#(length1(X)) -> a__length1#(X)
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__from(X) -> cons(mark(X),from(s(X)))
    a__length(nil()) -> 0()
    a__length(cons(X,Y)) -> s(a__length1(Y))
    a__length1(X) -> a__length(X)
    mark(from(X)) -> a__from(mark(X))
    mark(length(X)) -> a__length(X)
    mark(length1(X)) -> a__length1(X)
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    mark(0()) -> 0()
    a__from(X) -> from(X)
    a__length(X) -> length(X)
    a__length1(X) -> length1(X)
   graph:
    a__length1#(X) -> a__length#(X) ->
    a__length#(cons(X,Y)) -> a__length1#(Y)
    a__length#(cons(X,Y)) -> a__length1#(Y) ->
    a__length1#(X) -> a__length#(X)
    mark#(length1(X)) -> a__length1#(X) ->
    a__length1#(X) -> a__length#(X)
    mark#(length(X)) -> a__length#(X) ->
    a__length#(cons(X,Y)) -> a__length1#(Y)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length1(X)) -> a__length1#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    a__from#(X) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X)
   SCC Processor:
    #sccs: 2
    #rules: 7
    #arcs: 29/81
    DPs:
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> mark#(X)
     mark#(from(X)) -> a__from#(mark(X))
     a__from#(X) -> mark#(X)
     mark#(s(X)) -> mark#(X)
    TRS:
     a__from(X) -> cons(mark(X),from(s(X)))
     a__length(nil()) -> 0()
     a__length(cons(X,Y)) -> s(a__length1(Y))
     a__length1(X) -> a__length(X)
     mark(from(X)) -> a__from(mark(X))
     mark(length(X)) -> a__length(X)
     mark(length1(X)) -> a__length1(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__from(X) -> from(X)
     a__length(X) -> length(X)
     a__length1(X) -> length1(X)
    Matrix Interpretation Processor: dim=3
     
     interpretation:
      [mark#](x0) = [1 1 0]x0,
      
      [a__from#](x0) = [1 1 0]x0 + [1],
      
                      [0 0 0]     [0]
      [length1](x0) = [0 1 1]x0 + [1]
                      [0 0 0]     [0],
      
                     [0 0 0]     [0]
      [length](x0) = [0 1 1]x0 + [1]
                     [0 0 0]     [0],
      
                         [0 0 0]     [0]
      [a__length1](x0) = [0 1 1]x0 + [1]
                         [0 0 0]     [0],
      
            [0]
      [0] = [0]
            [0],
      
                        [0 0 0]     [0]
      [a__length](x0) = [0 1 1]x0 + [1]
                        [0 0 0]     [0],
      
              [0]
      [nil] = [0]
              [0],
      
                       [1 1 0]     [0 0 0]     [0]
      [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [1]
                       [0 0 0]     [0 1 0]     [0],
      
                   [1 1 0]     [1]
      [from](x0) = [0 0 0]x0 + [1]
                   [0 0 0]     [0],
      
                [1 0 0]     [0]
      [s](x0) = [0 1 0]x0 + [1]
                [0 0 0]     [0],
      
                        [0]
      [mark](x0) = x0 + [0]
                        [1],
      
                      [1 1 0]     [1]
      [a__from](x0) = [0 0 0]x0 + [1]
                      [0 0 0]     [1]
     orientation:
      mark#(cons(X1,X2)) = [1 1 0]X1 + [0 0 1]X2 + [1] >= [1 1 0]X1 = mark#(X1)
      
      mark#(from(X)) = [1 1 0]X + [2] >= [1 1 0]X = mark#(X)
      
      mark#(from(X)) = [1 1 0]X + [2] >= [1 1 0]X + [1] = a__from#(mark(X))
      
      a__from#(X) = [1 1 0]X + [1] >= [1 1 0]X = mark#(X)
      
      mark#(s(X)) = [1 1 0]X + [1] >= [1 1 0]X = mark#(X)
      
                   [1 1 0]    [1]    [1 1 0]    [0]                           
      a__from(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = cons(mark(X),from(s(X)))
                   [0 0 0]    [1]    [0 0 0]    [1]                           
      
                         [0]    [0]      
      a__length(nil()) = [1] >= [0] = 0()
                         [0]    [0]      
      
                             [0 0 0]    [0]    [0 0 0]    [0]                   
      a__length(cons(X,Y)) = [0 1 1]Y + [2] >= [0 1 1]Y + [2] = s(a__length1(Y))
                             [0 0 0]    [0]    [0 0 0]    [0]                   
      
                      [0 0 0]    [0]    [0 0 0]    [0]               
      a__length1(X) = [0 1 1]X + [1] >= [0 1 1]X + [1] = a__length(X)
                      [0 0 0]    [0]    [0 0 0]    [0]               
      
                      [1 1 0]    [1]    [1 1 0]    [1]                   
      mark(from(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__from(mark(X))
                      [0 0 0]    [1]    [0 0 0]    [1]                   
      
                        [0 0 0]    [0]    [0 0 0]    [0]               
      mark(length(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = a__length(X)
                        [0 0 0]    [1]    [0 0 0]    [0]               
      
                         [0 0 0]    [0]    [0 0 0]    [0]                
      mark(length1(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = a__length1(X)
                         [0 0 0]    [1]    [0 0 0]    [0]                
      
                          [1 1 0]     [0 0 0]     [0]    [1 1 0]     [0 0 0]     [0]                    
      mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 1]X2 + [1] >= [0 0 0]X1 + [0 0 1]X2 + [1] = cons(mark(X1),X2)
                          [0 0 0]     [0 1 0]     [1]    [0 0 0]     [0 1 0]     [0]                    
      
                   [1 0 0]    [0]    [1 0 0]    [0]             
      mark(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(mark(X))
                   [0 0 0]    [1]    [0 0 0]    [0]             
      
                    [0]    [0]        
      mark(nil()) = [0] >= [0] = nil()
                    [1]    [0]        
      
                  [0]    [0]      
      mark(0()) = [0] >= [0] = 0()
                  [1]    [0]      
      
                   [1 1 0]    [1]    [1 1 0]    [1]          
      a__from(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = from(X)
                   [0 0 0]    [1]    [0 0 0]    [0]          
      
                     [0 0 0]    [0]    [0 0 0]    [0]            
      a__length(X) = [0 1 1]X + [1] >= [0 1 1]X + [1] = length(X)
                     [0 0 0]    [0]    [0 0 0]    [0]            
      
                      [0 0 0]    [0]    [0 0 0]    [0]             
      a__length1(X) = [0 1 1]X + [1] >= [0 1 1]X + [1] = length1(X)
                      [0 0 0]    [0]    [0 0 0]    [0]             
     problem:
      DPs:
       
      TRS:
       a__from(X) -> cons(mark(X),from(s(X)))
       a__length(nil()) -> 0()
       a__length(cons(X,Y)) -> s(a__length1(Y))
       a__length1(X) -> a__length(X)
       mark(from(X)) -> a__from(mark(X))
       mark(length(X)) -> a__length(X)
       mark(length1(X)) -> a__length1(X)
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       mark(nil()) -> nil()
       mark(0()) -> 0()
       a__from(X) -> from(X)
       a__length(X) -> length(X)
       a__length1(X) -> length1(X)
     Qed
    
    DPs:
     a__length1#(X) -> a__length#(X)
     a__length#(cons(X,Y)) -> a__length1#(Y)
    TRS:
     a__from(X) -> cons(mark(X),from(s(X)))
     a__length(nil()) -> 0()
     a__length(cons(X,Y)) -> s(a__length1(Y))
     a__length1(X) -> a__length(X)
     mark(from(X)) -> a__from(mark(X))
     mark(length(X)) -> a__length(X)
     mark(length1(X)) -> a__length1(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__from(X) -> from(X)
     a__length(X) -> length(X)
     a__length1(X) -> length1(X)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [a__length1#](x0) = 1x0,
      
      [a__length#](x0) = x0,
      
      [length1](x0) = 2,
      
      [length](x0) = 0,
      
      [a__length1](x0) = 4,
      
      [0] = 0,
      
      [a__length](x0) = 1,
      
      [nil] = 2,
      
      [cons](x0, x1) = 2x1 + 0,
      
      [from](x0) = 3,
      
      [s](x0) = 0,
      
      [mark](x0) = 4x0 + 0,
      
      [a__from](x0) = 6
     orientation:
      a__length1#(X) = 1X >= X = a__length#(X)
      
      a__length#(cons(X,Y)) = 2Y + 0 >= 1Y = a__length1#(Y)
      
      a__from(X) = 6 >= 5 = cons(mark(X),from(s(X)))
      
      a__length(nil()) = 1 >= 0 = 0()
      
      a__length(cons(X,Y)) = 1 >= 0 = s(a__length1(Y))
      
      a__length1(X) = 4 >= 1 = a__length(X)
      
      mark(from(X)) = 7 >= 6 = a__from(mark(X))
      
      mark(length(X)) = 4 >= 1 = a__length(X)
      
      mark(length1(X)) = 6 >= 4 = a__length1(X)
      
      mark(cons(X1,X2)) = 6X2 + 4 >= 2X2 + 0 = cons(mark(X1),X2)
      
      mark(s(X)) = 4 >= 0 = s(mark(X))
      
      mark(nil()) = 6 >= 2 = nil()
      
      mark(0()) = 4 >= 0 = 0()
      
      a__from(X) = 6 >= 3 = from(X)
      
      a__length(X) = 1 >= 0 = length(X)
      
      a__length1(X) = 4 >= 2 = length1(X)
     problem:
      DPs:
       
      TRS:
       a__from(X) -> cons(mark(X),from(s(X)))
       a__length(nil()) -> 0()
       a__length(cons(X,Y)) -> s(a__length1(Y))
       a__length1(X) -> a__length(X)
       mark(from(X)) -> a__from(mark(X))
       mark(length(X)) -> a__length(X)
       mark(length1(X)) -> a__length1(X)
       mark(cons(X1,X2)) -> cons(mark(X1),X2)
       mark(s(X)) -> s(mark(X))
       mark(nil()) -> nil()
       mark(0()) -> 0()
       a__from(X) -> from(X)
       a__length(X) -> length(X)
       a__length1(X) -> length1(X)
     Qed