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)

max/plus interpretations on N:

  a__nats_A = 13
  a__nats#_A = 20
  a__adx_A(x1) = max{1, x1}
  a__adx#_A(x1) = max{3, 2 + x1}
  a__zeros_A = 13
  a__zeros#_A = 15
  cons_A(x1,x2) = max{0, 12 + x1, -3 + x2}
  cons#_A(x1,x2) = max{14, 1, 6}
  0_A = 1
  0#_A = 3
  zeros_A = 10
  zeros#_A = 0
  a__incr_A(x1) = max{11, x1}
  a__incr#_A(x1) = max{14, 3}
  s_A(x1) = max{0, -15}
  s#_A(x1) = max{2, -6}
  incr_A(x1) = max{11, x1}
  incr#_A(x1) = max{5, 9}
  adx_A(x1) = max{0, x1}
  adx#_A(x1) = max{0, -2}
  a__hd_A(x1) = max{4, 2 + x1}
  a__hd#_A(x1) = max{11, -1 + x1}
  mark_A(x1) = max{0, 3 + x1}
  mark#_A(x1) = max{4, 10 + x1}
  a__tl_A(x1) = max{0, 11 + x1}
  a__tl#_A(x1) = max{8, 13 + x1}
  nats_A = 10
  nats#_A = 0
  hd_A(x1) = max{0, 2 + x1}
  hd#_A(x1) = max{3, -2}
  tl_A(x1) = max{7, 11 + x1}
  tl#_A(x1) = max{9, 7}

precedence:

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