YES

TRS:

  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)

linear polynomial interpretations on N:

  a__nats_A = 4
  a__nats#_A = 5
  a__adx_A(x1) = x1 + 1
  a__adx#_A(x1) = 4
  a__zeros_A = 3
  a__zeros#_A = 2
  cons_A(x1,x2) = x1 + x2 + 1
  cons#_A(x1,x2) = 1
  0_A = 1
  0#_A = 0
  zeros_A = 1
  zeros#_A = 0
  a__incr_A(x1) = x1
  a__incr#_A(x1) = 3
  s_A(x1) = x1
  s#_A(x1) = 0
  incr_A(x1) = x1
  incr#_A(x1) = 2
  adx_A(x1) = x1 + 1
  adx#_A(x1) = 3
  a__hd_A(x1) = x1 + 5
  a__hd#_A(x1) = x1 + 6
  mark_A(x1) = x1 + 3
  mark#_A(x1) = x1 + 5
  a__tl_A(x1) = x1 + 4
  a__tl#_A(x1) = x1 + 5
  nats_A = 1
  nats#_A = 4
  hd_A(x1) = x1 + 5
  hd#_A(x1) = x1 + 5
  tl_A(x1) = x1 + 4
  tl#_A(x1) = 4

precedence:

  nats > a__nats > a__adx = a__zeros > cons = zeros = hd > a__hd = mark = a__tl > a__incr = tl > 0 = s = incr = adx