MAYBE

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

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

We add following dependency tuples:

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

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

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

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

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

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

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

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

The input cannot be shown compatible

Arrrr..