MAYBE

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

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

We add following dependency tuples:

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

and mark the set of starting terms.

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

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

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

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

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

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

{ fib^#(0()) -> c_1()
, fib^#(s(0())) -> c_2()
, +^#(x, 0()) -> c_4() }

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

Strict DPs:
  { fib^#(s(s(x))) ->
    c_3(+^#(fib(s(x)), fib(x)), fib^#(s(x)), fib^#(x))
  , +^#(x, s(y)) -> c_5(+^#(x, y)) }
Weak Trs:
  { fib(0()) -> 0()
  , fib(s(0())) -> s(0())
  , fib(s(s(x))) -> +(fib(s(x)), fib(x))
  , +(x, 0()) -> x
  , +(x, s(y)) -> s(+(x, y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..