MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

Strict DPs:
  { +^#(X, s(Y)) -> c_2(+^#(X, Y))
  , f^#(0(), s(0()), X) -> c_3(f^#(X, +(X, X), X), +^#(X, X)) }
Weak DPs:
  { +^#(X, 0()) -> c_1()
  , g^#(X, Y) -> c_4()
  , g^#(X, Y) -> c_5() }
Weak Trs:
  { +(X, 0()) -> X
  , +(X, s(Y)) -> s(+(X, Y))
  , f(0(), s(0()), X) -> f(X, +(X, X), X)
  , g(X, Y) -> X
  , g(X, Y) -> Y }
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.

{ +^#(X, 0()) -> c_1()
, g^#(X, Y) -> c_4()
, g^#(X, Y) -> c_5() }

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

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

We replace rewrite rules by usable rules:

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

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

Strict DPs:
  { +^#(X, s(Y)) -> c_2(+^#(X, Y))
  , f^#(0(), s(0()), X) -> c_3(f^#(X, +(X, X), X), +^#(X, X)) }
Weak Trs:
  { +(X, 0()) -> X
  , +(X, s(Y)) -> s(+(X, Y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..