MAYBE

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

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

We add following dependency tuples:

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

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

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

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

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

{ p^#(s(0())) -> c_3() }

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

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

We replace rewrite rules by usable rules:

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

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

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

The input cannot be shown compatible

Arrrr..