MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

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

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

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { g(s(x), s(y)) -> g(x, y)
    , g(s(x), 0()) -> t() }

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

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

The input cannot be shown compatible

Arrrr..