MAYBE

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

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

We add following dependency tuples:

Strict DPs:
  { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x)))
  , round^#(s(s(x))) -> c_2(round^#(x))
  , round^#(s(0())) -> c_3()
  , round^#(0()) -> c_4()
  , round^#(0()) -> c_5() }

and mark the set of starting terms.

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

Strict DPs:
  { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x)))
  , round^#(s(s(x))) -> c_2(round^#(x))
  , round^#(s(0())) -> c_3()
  , round^#(0()) -> c_4()
  , round^#(0()) -> c_5() }
Weak Trs:
  { f(s(x), x) -> f(s(x), round(s(x)))
  , round(s(s(x))) -> s(s(round(x)))
  , round(s(0())) -> s(0())
  , round(0()) -> s(0())
  , round(0()) -> 0() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {3,4,5} by applications of
Pre({3,4,5}) = {1,2}. Here rules are labeled as follows:

  DPs:
    { 1: f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x)))
    , 2: round^#(s(s(x))) -> c_2(round^#(x))
    , 3: round^#(s(0())) -> c_3()
    , 4: round^#(0()) -> c_4()
    , 5: round^#(0()) -> c_5() }

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

Strict DPs:
  { f^#(s(x), x) -> c_1(f^#(s(x), round(s(x))), round^#(s(x)))
  , round^#(s(s(x))) -> c_2(round^#(x)) }
Weak DPs:
  { round^#(s(0())) -> c_3()
  , round^#(0()) -> c_4()
  , round^#(0()) -> c_5() }
Weak Trs:
  { f(s(x), x) -> f(s(x), round(s(x)))
  , round(s(s(x))) -> s(s(round(x)))
  , round(s(0())) -> s(0())
  , round(0()) -> s(0())
  , round(0()) -> 0() }
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.

{ round^#(s(0())) -> c_3()
, round^#(0()) -> c_4()
, round^#(0()) -> c_5() }

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

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

We replace rewrite rules by usable rules:

  Weak Usable Rules:
    { round(s(s(x))) -> s(s(round(x)))
    , round(s(0())) -> s(0())
    , round(0()) -> s(0())
    , round(0()) -> 0() }

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

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

The input cannot be shown compatible

Arrrr..