MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { a__dbl(X) -> dbl(X)
  , a__dbl(0()) -> 0()
  , a__dbl(s(X)) -> s(s(dbl(X)))
  , a__dbls(X) -> dbls(X)
  , a__dbls(nil()) -> nil()
  , a__dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y))
  , a__sel(X1, X2) -> sel(X1, X2)
  , a__sel(0(), cons(X, Y)) -> mark(X)
  , a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z))
  , mark(0()) -> 0()
  , mark(s(X)) -> s(X)
  , mark(dbl(X)) -> a__dbl(mark(X))
  , mark(nil()) -> nil()
  , mark(cons(X1, X2)) -> cons(X1, X2)
  , mark(dbls(X)) -> a__dbls(mark(X))
  , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
  , mark(indx(X1, X2)) -> a__indx(mark(X1), X2)
  , mark(from(X)) -> a__from(X)
  , mark(01()) -> 01()
  , mark(s1(X)) -> s1(mark(X))
  , mark(dbl1(X)) -> a__dbl1(mark(X))
  , mark(sel1(X1, X2)) -> a__sel1(mark(X1), mark(X2))
  , mark(quote(X)) -> a__quote(mark(X))
  , a__indx(X1, X2) -> indx(X1, X2)
  , a__indx(nil(), X) -> nil()
  , a__indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z))
  , a__from(X) -> cons(X, from(s(X)))
  , a__from(X) -> from(X)
  , a__dbl1(X) -> dbl1(X)
  , a__dbl1(0()) -> 01()
  , a__dbl1(s(X)) -> s1(s1(a__dbl1(mark(X))))
  , a__sel1(X1, X2) -> sel1(X1, X2)
  , a__sel1(0(), cons(X, Y)) -> mark(X)
  , a__sel1(s(X), cons(Y, Z)) -> a__sel1(mark(X), mark(Z))
  , a__quote(X) -> quote(X)
  , a__quote(0()) -> 01()
  , a__quote(s(X)) -> s1(a__quote(mark(X)))
  , a__quote(dbl(X)) -> a__dbl1(mark(X))
  , a__quote(sel(X, Y)) -> a__sel1(mark(X), mark(Y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..