MAYBE

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

Strict Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(x, s(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

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

and mark the set of starting terms.

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

Strict DPs:
  { f^#(0()) -> c_1()
  , f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
  , f^#(s(x)) -> c_3(f^#(x), f^#(x))
  , g^#(x) -> c_4() }
Weak Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(x, s(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

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

  DPs:
    { 1: f^#(0()) -> c_1()
    , 2: f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
    , 3: f^#(s(x)) -> c_3(f^#(x), f^#(x))
    , 4: g^#(x) -> c_4() }

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

Strict DPs:
  { f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
  , f^#(s(x)) -> c_3(f^#(x), f^#(x)) }
Weak DPs:
  { f^#(0()) -> c_1()
  , g^#(x) -> c_4() }
Weak Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(x, s(x)) }
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.

{ f^#(0()) -> c_1()
, g^#(x) -> c_4() }

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

Strict DPs:
  { f^#(s(x)) -> c_2(g^#(f(x)), f^#(x))
  , f^#(s(x)) -> c_3(f^#(x), f^#(x)) }
Weak Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(x, s(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { f^#(s(x)) -> c_2(g^#(f(x)), f^#(x)) }

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

Strict DPs:
  { f^#(s(x)) -> c_1(f^#(x), f^#(x))
  , f^#(s(x)) -> c_2(f^#(x)) }
Weak Trs:
  { f(0()) -> 1()
  , f(s(x)) -> g(f(x))
  , f(s(x)) -> +(f(x), s(f(x)))
  , g(x) -> +(x, s(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

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

Strict DPs:
  { f^#(s(x)) -> c_1(f^#(x), f^#(x))
  , f^#(s(x)) -> c_2(f^#(x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..