YES

Problem:
 a__nats() -> a__adx(a__zeros())
 a__zeros() -> cons(0(),zeros())
 a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
 a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
 a__hd(cons(X,Y)) -> mark(X)
 a__tl(cons(X,Y)) -> mark(Y)
 mark(nats()) -> a__nats()
 mark(adx(X)) -> a__adx(mark(X))
 mark(zeros()) -> a__zeros()
 mark(incr(X)) -> a__incr(mark(X))
 mark(hd(X)) -> a__hd(mark(X))
 mark(tl(X)) -> a__tl(mark(X))
 mark(cons(X1,X2)) -> cons(X1,X2)
 mark(0()) -> 0()
 mark(s(X)) -> s(X)
 a__nats() -> nats()
 a__adx(X) -> adx(X)
 a__zeros() -> zeros()
 a__incr(X) -> incr(X)
 a__hd(X) -> hd(X)
 a__tl(X) -> tl(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [tl](x0) = 2x0 + 3,
   
   [hd](x0) = x0 + 3,
   
   [nats] = 0,
   
   [a__tl](x0) = 2x0 + 3,
   
   [mark](x0) = 3x0 + 4,
   
   [a__hd](x0) = x0 + 3,
   
   [adx](x0) = x0,
   
   [incr](x0) = x0,
   
   [s](x0) = x0,
   
   [a__incr](x0) = x0,
   
   [cons](x0, x1) = 4x0 + 4x1 + 2,
   
   [zeros] = 0,
   
   [0] = 0,
   
   [a__adx](x0) = x0,
   
   [a__zeros] = 4,
   
   [a__nats] = 4
  orientation:
   a__nats() = 4 >= 4 = a__adx(a__zeros())
   
   a__zeros() = 4 >= 2 = cons(0(),zeros())
   
   a__incr(cons(X,Y)) = 4X + 4Y + 2 >= 4X + 4Y + 2 = cons(s(X),incr(Y))
   
   a__adx(cons(X,Y)) = 4X + 4Y + 2 >= 4X + 4Y + 2 = a__incr(cons(X,adx(Y)))
   
   a__hd(cons(X,Y)) = 4X + 4Y + 5 >= 3X + 4 = mark(X)
   
   a__tl(cons(X,Y)) = 8X + 8Y + 7 >= 3Y + 4 = mark(Y)
   
   mark(nats()) = 4 >= 4 = a__nats()
   
   mark(adx(X)) = 3X + 4 >= 3X + 4 = a__adx(mark(X))
   
   mark(zeros()) = 4 >= 4 = a__zeros()
   
   mark(incr(X)) = 3X + 4 >= 3X + 4 = a__incr(mark(X))
   
   mark(hd(X)) = 3X + 13 >= 3X + 7 = a__hd(mark(X))
   
   mark(tl(X)) = 6X + 13 >= 6X + 11 = a__tl(mark(X))
   
   mark(cons(X1,X2)) = 12X1 + 12X2 + 10 >= 4X1 + 4X2 + 2 = cons(X1,X2)
   
   mark(0()) = 4 >= 0 = 0()
   
   mark(s(X)) = 3X + 4 >= X = s(X)
   
   a__nats() = 4 >= 0 = nats()
   
   a__adx(X) = X >= X = adx(X)
   
   a__zeros() = 4 >= 0 = zeros()
   
   a__incr(X) = X >= X = incr(X)
   
   a__hd(X) = X + 3 >= X + 3 = hd(X)
   
   a__tl(X) = 2X + 3 >= 2X + 3 = tl(X)
  problem:
   a__nats() -> a__adx(a__zeros())
   a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
   a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
   mark(nats()) -> a__nats()
   mark(adx(X)) -> a__adx(mark(X))
   mark(zeros()) -> a__zeros()
   mark(incr(X)) -> a__incr(mark(X))
   a__adx(X) -> adx(X)
   a__incr(X) -> incr(X)
   a__hd(X) -> hd(X)
   a__tl(X) -> tl(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [tl](x0) = x0,
    
    [hd](x0) = 2x0,
    
    [nats] = 2,
    
    [a__tl](x0) = x0,
    
    [mark](x0) = x0,
    
    [a__hd](x0) = 2x0,
    
    [adx](x0) = x0,
    
    [incr](x0) = x0,
    
    [s](x0) = x0,
    
    [a__incr](x0) = x0,
    
    [cons](x0, x1) = 2x0 + 2x1,
    
    [zeros] = 5,
    
    [a__adx](x0) = x0,
    
    [a__zeros] = 2,
    
    [a__nats] = 2
   orientation:
    a__nats() = 2 >= 2 = a__adx(a__zeros())
    
    a__incr(cons(X,Y)) = 2X + 2Y >= 2X + 2Y = cons(s(X),incr(Y))
    
    a__adx(cons(X,Y)) = 2X + 2Y >= 2X + 2Y = a__incr(cons(X,adx(Y)))
    
    mark(nats()) = 2 >= 2 = a__nats()
    
    mark(adx(X)) = X >= X = a__adx(mark(X))
    
    mark(zeros()) = 5 >= 2 = a__zeros()
    
    mark(incr(X)) = X >= X = a__incr(mark(X))
    
    a__adx(X) = X >= X = adx(X)
    
    a__incr(X) = X >= X = incr(X)
    
    a__hd(X) = 2X >= 2X = hd(X)
    
    a__tl(X) = X >= X = tl(X)
   problem:
    a__nats() -> a__adx(a__zeros())
    a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
    a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
    mark(nats()) -> a__nats()
    mark(adx(X)) -> a__adx(mark(X))
    mark(incr(X)) -> a__incr(mark(X))
    a__adx(X) -> adx(X)
    a__incr(X) -> incr(X)
    a__hd(X) -> hd(X)
    a__tl(X) -> tl(X)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [tl](x0) = 4x0,
     
     [hd](x0) = 2x0,
     
     [nats] = 0,
     
     [a__tl](x0) = 4x0 + 1,
     
     [mark](x0) = x0,
     
     [a__hd](x0) = 2x0,
     
     [adx](x0) = x0,
     
     [incr](x0) = x0,
     
     [s](x0) = x0,
     
     [a__incr](x0) = x0,
     
     [cons](x0, x1) = 4x0 + 4x1,
     
     [a__adx](x0) = x0,
     
     [a__zeros] = 0,
     
     [a__nats] = 0
    orientation:
     a__nats() = 0 >= 0 = a__adx(a__zeros())
     
     a__incr(cons(X,Y)) = 4X + 4Y >= 4X + 4Y = cons(s(X),incr(Y))
     
     a__adx(cons(X,Y)) = 4X + 4Y >= 4X + 4Y = a__incr(cons(X,adx(Y)))
     
     mark(nats()) = 0 >= 0 = a__nats()
     
     mark(adx(X)) = X >= X = a__adx(mark(X))
     
     mark(incr(X)) = X >= X = a__incr(mark(X))
     
     a__adx(X) = X >= X = adx(X)
     
     a__incr(X) = X >= X = incr(X)
     
     a__hd(X) = 2X >= 2X = hd(X)
     
     a__tl(X) = 4X + 1 >= 4X = tl(X)
    problem:
     a__nats() -> a__adx(a__zeros())
     a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
     a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
     mark(nats()) -> a__nats()
     mark(adx(X)) -> a__adx(mark(X))
     mark(incr(X)) -> a__incr(mark(X))
     a__adx(X) -> adx(X)
     a__incr(X) -> incr(X)
     a__hd(X) -> hd(X)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [hd](x0) = 4x0,
      
      [nats] = 6,
      
      [mark](x0) = 2x0 + 7,
      
      [a__hd](x0) = 6x0 + 2,
      
      [adx](x0) = x0 + 2,
      
      [incr](x0) = x0 + 2,
      
      [s](x0) = x0,
      
      [a__incr](x0) = x0 + 2,
      
      [cons](x0, x1) = x0 + x1 + 6,
      
      [a__adx](x0) = x0 + 4,
      
      [a__zeros] = 0,
      
      [a__nats] = 4
     orientation:
      a__nats() = 4 >= 4 = a__adx(a__zeros())
      
      a__incr(cons(X,Y)) = X + Y + 8 >= X + Y + 8 = cons(s(X),incr(Y))
      
      a__adx(cons(X,Y)) = X + Y + 10 >= X + Y + 10 = a__incr(cons(X,adx(Y)))
      
      mark(nats()) = 19 >= 4 = a__nats()
      
      mark(adx(X)) = 2X + 11 >= 2X + 11 = a__adx(mark(X))
      
      mark(incr(X)) = 2X + 11 >= 2X + 9 = a__incr(mark(X))
      
      a__adx(X) = X + 4 >= X + 2 = adx(X)
      
      a__incr(X) = X + 2 >= X + 2 = incr(X)
      
      a__hd(X) = 6X + 2 >= 4X = hd(X)
     problem:
      a__nats() -> a__adx(a__zeros())
      a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
      a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
      mark(adx(X)) -> a__adx(mark(X))
      a__incr(X) -> incr(X)
     DP Processor:
      DPs:
       a__nats#() -> a__adx#(a__zeros())
       a__adx#(cons(X,Y)) -> a__incr#(cons(X,adx(Y)))
       mark#(adx(X)) -> mark#(X)
       mark#(adx(X)) -> a__adx#(mark(X))
      TRS:
       a__nats() -> a__adx(a__zeros())
       a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
       a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
       mark(adx(X)) -> a__adx(mark(X))
       a__incr(X) -> incr(X)
      TDG Processor:
       DPs:
        a__nats#() -> a__adx#(a__zeros())
        a__adx#(cons(X,Y)) -> a__incr#(cons(X,adx(Y)))
        mark#(adx(X)) -> mark#(X)
        mark#(adx(X)) -> a__adx#(mark(X))
       TRS:
        a__nats() -> a__adx(a__zeros())
        a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
        a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
        mark(adx(X)) -> a__adx(mark(X))
        a__incr(X) -> incr(X)
       graph:
        mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> a__adx#(mark(X))
        mark#(adx(X)) -> mark#(X) -> mark#(adx(X)) -> mark#(X)
        mark#(adx(X)) -> a__adx#(mark(X)) ->
        a__adx#(cons(X,Y)) -> a__incr#(cons(X,adx(Y)))
        a__nats#() -> a__adx#(a__zeros()) -> a__adx#(cons(X,Y)) -> a__incr#(cons(X,adx(Y)))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 4/16
        DPs:
         mark#(adx(X)) -> mark#(X)
        TRS:
         a__nats() -> a__adx(a__zeros())
         a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
         a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
         mark(adx(X)) -> a__adx(mark(X))
         a__incr(X) -> incr(X)
        Subterm Criterion Processor:
         simple projection:
          pi(mark#) = 0
         problem:
          DPs:
           
          TRS:
           a__nats() -> a__adx(a__zeros())
           a__incr(cons(X,Y)) -> cons(s(X),incr(Y))
           a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y)))
           mark(adx(X)) -> a__adx(mark(X))
           a__incr(X) -> incr(X)
         Qed