MAYBE

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

Strict Trs:
  { f(X) -> cons(X, f(g(X)))
  , g(0()) -> s(0())
  , g(s(X)) -> s(s(g(X)))
  , sel(0(), cons(X, Y)) -> X
  , sel(s(X), cons(Y, Z)) -> sel(X, Z) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { f^#(X) -> c_1(f^#(g(X)), g^#(X))
  , g^#(0()) -> c_2()
  , g^#(s(X)) -> c_3(g^#(X))
  , sel^#(0(), cons(X, Y)) -> c_4()
  , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(X) -> c_1(f^#(g(X)), g^#(X))
  , g^#(0()) -> c_2()
  , g^#(s(X)) -> c_3(g^#(X))
  , sel^#(0(), cons(X, Y)) -> c_4()
  , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) }
Weak Trs:
  { f(X) -> cons(X, f(g(X)))
  , g(0()) -> s(0())
  , g(s(X)) -> s(s(g(X)))
  , sel(0(), cons(X, Y)) -> X
  , sel(s(X), cons(Y, Z)) -> sel(X, Z) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {2,4} by applications of
Pre({2,4}) = {1,3,5}. Here rules are labeled as follows:

  DPs:
    { 1: f^#(X) -> c_1(f^#(g(X)), g^#(X))
    , 2: g^#(0()) -> c_2()
    , 3: g^#(s(X)) -> c_3(g^#(X))
    , 4: sel^#(0(), cons(X, Y)) -> c_4()
    , 5: sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) }

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

Strict DPs:
  { f^#(X) -> c_1(f^#(g(X)), g^#(X))
  , g^#(s(X)) -> c_3(g^#(X))
  , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) }
Weak DPs:
  { g^#(0()) -> c_2()
  , sel^#(0(), cons(X, Y)) -> c_4() }
Weak Trs:
  { f(X) -> cons(X, f(g(X)))
  , g(0()) -> s(0())
  , g(s(X)) -> s(s(g(X)))
  , sel(0(), cons(X, Y)) -> X
  , sel(s(X), cons(Y, Z)) -> sel(X, Z) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ g^#(0()) -> c_2()
, sel^#(0(), cons(X, Y)) -> c_4() }

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

Strict DPs:
  { f^#(X) -> c_1(f^#(g(X)), g^#(X))
  , g^#(s(X)) -> c_3(g^#(X))
  , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) }
Weak Trs:
  { f(X) -> cons(X, f(g(X)))
  , g(0()) -> s(0())
  , g(s(X)) -> s(s(g(X)))
  , sel(0(), cons(X, Y)) -> X
  , sel(s(X), cons(Y, Z)) -> sel(X, Z) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { g(0()) -> s(0())
    , g(s(X)) -> s(s(g(X))) }

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

Strict DPs:
  { f^#(X) -> c_1(f^#(g(X)), g^#(X))
  , g^#(s(X)) -> c_3(g^#(X))
  , sel^#(s(X), cons(Y, Z)) -> c_5(sel^#(X, Z)) }
Weak Trs:
  { g(0()) -> s(0())
  , g(s(X)) -> s(s(g(X))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..