YES

TRS:

  a__eq(0(),0()) -> true()
  a__eq(s(X),s(Y)) -> a__eq(X,Y)
  a__eq(X,Y) -> false()
  a__inf(X) -> cons(X,inf(s(X)))
  a__take(0(),X) -> nil()
  a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
  a__length(nil()) -> 0()
  a__length(cons(X,L)) -> s(length(L))
  mark(eq(X1,X2)) -> a__eq(X1,X2)
  mark(inf(X)) -> a__inf(mark(X))
  mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
  mark(length(X)) -> a__length(mark(X))
  mark(0()) -> 0()
  mark(true()) -> true()
  mark(s(X)) -> s(X)
  mark(false()) -> false()
  mark(cons(X1,X2)) -> cons(X1,X2)
  mark(nil()) -> nil()
  a__eq(X1,X2) -> eq(X1,X2)
  a__inf(X) -> inf(X)
  a__take(X1,X2) -> take(X1,X2)
  a__length(X) -> length(X)

max/plus interpretations on N:

  a__eq_A(x1,x2) = max{0, x1, x2}
  a__eq#_A(x1,x2) = max{0, x1, x2}
  0_A = 0
  0#_A = 0
  true_A = 0
  true#_A = 0
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  false_A = 0
  false#_A = 0
  a__inf_A(x1) = max{0, x1}
  a__inf#_A(x1) = max{0, x1}
  cons_A(x1,x2) = max{0, x1, x2}
  cons#_A(x1,x2) = max{0, x1, x2}
  inf_A(x1) = max{0, x1}
  inf#_A(x1) = max{0, x1}
  a__take_A(x1,x2) = max{0, x1, x2}
  a__take#_A(x1,x2) = max{0, x1, x2}
  nil_A = 0
  nil#_A = 0
  take_A(x1,x2) = max{0, x1, x2}
  take#_A(x1,x2) = max{0, x1, x2}
  a__length_A(x1) = max{0, x1}
  a__length#_A(x1) = max{0, x1}
  length_A(x1) = max{0, x1}
  length#_A(x1) = max{0, x1}
  mark_A(x1) = max{0, x1}
  mark#_A(x1) = max{0, x1}
  eq_A(x1,x2) = max{0, x1, x2}
  eq#_A(x1,x2) = max{0, x1, x2}

precedence:

  a__eq = false = mark > a__inf = a__take = nil = eq > 0 = cons = inf = take > true = s > a__length > length