MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

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

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

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { f(x, s(y)) -> f(x, y)
    , f(s(x), y) -> f(x, y)
    , f(0(), 0()) -> tt() }

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

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

The input cannot be shown compatible

Arrrr..