MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

{ f^#(x, y) -> c_3() }

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

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

The input cannot be shown compatible

Arrrr..