YES

TRS:

  a__incr(nil()) -> nil()
  a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L))
  a__adx(nil()) -> nil()
  a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L)))
  a__nats() -> a__adx(a__zeros())
  a__zeros() -> cons(0(),zeros())
  a__head(cons(X,L)) -> mark(X)
  a__tail(cons(X,L)) -> mark(L)
  mark(incr(X)) -> a__incr(mark(X))
  mark(adx(X)) -> a__adx(mark(X))
  mark(nats()) -> a__nats()
  mark(zeros()) -> a__zeros()
  mark(head(X)) -> a__head(mark(X))
  mark(tail(X)) -> a__tail(mark(X))
  mark(nil()) -> nil()
  mark(cons(X1,X2)) -> cons(mark(X1),X2)
  mark(s(X)) -> s(mark(X))
  mark(0()) -> 0()
  a__incr(X) -> incr(X)
  a__adx(X) -> adx(X)
  a__nats() -> nats()
  a__zeros() -> zeros()
  a__head(X) -> head(X)
  a__tail(X) -> tail(X)

max/plus interpretations on N:

  a__incr_A(x1) = max{19, x1}
  a__incr#_A(x1) = max{29, 7 + x1}
  nil_A = 0
  nil#_A = 31
  cons_A(x1,x2) = max{13, 11 + x1, -5 + x2}
  cons#_A(x1,x2) = max{23, 1, -1}
  s_A(x1) = max{8, x1}
  s#_A(x1) = max{24, 19}
  mark_A(x1) = max{2, x1}
  mark#_A(x1) = max{22, 17 + x1}
  incr_A(x1) = max{19, x1}
  incr#_A(x1) = max{0, 21}
  a__adx_A(x1) = max{27, 15 + x1}
  a__adx#_A(x1) = max{30, 29 + x1}
  adx_A(x1) = max{27, 15 + x1}
  adx#_A(x1) = max{30, -2}
  a__nats_A = 28
  a__nats#_A = 44
  a__zeros_A = 13
  a__zeros#_A = 24
  0_A = 1
  0#_A = 0
  zeros_A = 13
  zeros#_A = 0
  a__head_A(x1) = max{8, x1}
  a__head#_A(x1) = max{24, 16 + x1}
  a__tail_A(x1) = max{14, 12 + x1}
  a__tail#_A(x1) = max{18, 28 + x1}
  nats_A = 28
  nats#_A = 0
  head_A(x1) = max{8, x1}
  head#_A(x1) = max{23, 23}
  tail_A(x1) = max{14, 12 + x1}
  tail#_A(x1) = max{0, 0}

precedence:

  a__adx > cons > a__incr = a__tail > mark > nil = s = incr = adx = a__nats = a__head = tail > a__zeros = nats = head > 0 = zeros