MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

{ id^#(0()) -> c_3() }

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

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

We replace rewrite rules by usable rules:

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

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

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

The input cannot be shown compatible

Arrrr..