MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { f^#(g(X)) -> c_1(f^#(f(X)), f^#(X))
  , f^#(h(X)) -> c_2() }

and mark the set of starting terms.

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

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

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

  DPs:
    { 1: f^#(g(X)) -> c_1(f^#(f(X)), f^#(X))
    , 2: f^#(h(X)) -> c_2() }

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

Strict DPs: { f^#(g(X)) -> c_1(f^#(f(X)), f^#(X)) }
Weak DPs: { f^#(h(X)) -> c_2() }
Weak Trs:
  { f(g(X)) -> g(f(f(X)))
  , f(h(X)) -> h(g(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^#(h(X)) -> c_2() }

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

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

The input cannot be shown compatible

Arrrr..