MAYBE

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

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

We add following dependency tuples:

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

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

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

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

Strict DPs:
  { f^#(s(x)) -> c_1(f^#(f(p(s(x)))), f^#(p(s(x))), p^#(s(x))) }
Weak DPs:
  { f^#(0()) -> c_2()
  , p^#(s(x)) -> c_3() }
Weak Trs:
  { f(s(x)) -> s(f(f(p(s(x)))))
  , f(0()) -> 0()
  , p(s(x)) -> 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_2()
, p^#(s(x)) -> c_3() }

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

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

Due to missing edges in the dependency-graph, the right-hand sides
of following rules could be simplified:

  { f^#(s(x)) -> c_1(f^#(f(p(s(x)))), f^#(p(s(x))), p^#(s(x))) }

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

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

The input cannot be shown compatible

Arrrr..