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{4, x1}
  a__incr#_A(x1) = max{4, x1}
  nil_A = 0
  nil#_A = 0
  cons_A(x1,x2) = max{2, 4 + x1, x2}
  cons#_A(x1,x2) = max{2, 4 + x1, x2}
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  mark_A(x1) = max{0, x1}
  mark#_A(x1) = max{0, x1}
  incr_A(x1) = max{4, x1}
  incr#_A(x1) = max{4, x1}
  a__adx_A(x1) = max{5, 3 + x1}
  a__adx#_A(x1) = max{5, 3 + x1}
  adx_A(x1) = max{5, 3 + x1}
  adx#_A(x1) = max{5, 3 + x1}
  a__nats_A = 8
  a__nats#_A = 8
  a__zeros_A = 5
  a__zeros#_A = 5
  0_A = 0
  0#_A = 0
  zeros_A = 5
  zeros#_A = 5
  a__head_A(x1) = max{1, 1 + x1}
  a__head#_A(x1) = max{1, 1 + x1}
  a__tail_A(x1) = max{1, 1 + x1}
  a__tail#_A(x1) = max{1, 1 + x1}
  nats_A = 8
  nats#_A = 8
  head_A(x1) = max{1, 1 + x1}
  head#_A(x1) = max{1, 1 + x1}
  tail_A(x1) = max{1, 1 + x1}
  tail#_A(x1) = max{1, 1 + x1}

precedence:

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